Wow, there is a lot to talk about.
Dragonborn:
This is just a raw improvement on every level. The old dragonborn (in the PHB) had a 2d6, action, breath weapon and resistance. And they were limited to the five options. Now, there are 10 options and more resistance to go around, plus the damage is improved. I like the change to making them an attack action, opens up a lot of options and makes this useful for the classic melee Dragonborn builds.
One thing I would change for certain, is I would make the cone or the line an option. Pick when you get the race, and you stick with it. I also... man I don't like Brass being on the list. This is a minor minor quibble, but it is playing second fiddle to gold and they are identical. That bugs me.
Another thing I'm not sold on, I'm not sure about prof per day. I might prefer something like 3 per short rest. I want this to feel like a tool they can pull out with some reliability. That might be too powerful, but I want them to feel like using their breath is a go to choice.
Then each of them gets 1 new ability (with Gem getting two)
Chromatics get to use an action to be immune for 10 minutes, and I love this. This is bad-assery that I want, to be able to use this to just stroll into a volcanic heart or something similar immune to the elemental forces. That screams dragon. 1/day feels appropriate too.
Metallics.... get jipped I think. They get a 1/day second breath. Not that they can't be potentially powerful options. Incapacitated can buy a round of safety from whatever failed, and the push back is nice since it is far enough away to be an escape button, but.... I don't know. It may grow on me. But it feels like it is very situationally useful and is going to get saved for "emergencies".
Gems get two. 30 ft telepathy (one-way, but I'm going to ignore that just like I do for GOOlocks) and 1 minute of flight. Both solid abilities, nothing super interesting though. The flavor is insane for the Wings, I love that to death.
Kobolds
This is kind of not what I expected. One thing I sort of like is how they talk about the roaring. "The roar of a kobold can express a range of emotion: anger, resolve, elation, fear, and more. " Roaring in fear? That's not something I've heard a lot. I might not make it a roar, because that feels like it should be a deeper sound, but it is interesting.
But, mechanics are more important here, and they are actually really really solid.
Sunlight sensitivity is gone, and you get a choice of one of three perks. 1) You have advantage against fear. Now, I know a lot of people don't like this because Kobold = Coward to them, but I've never liked Kobolds as cowards. And, even if they are cowards, this kind of fits still. Cowards are used to fear, it is a familiar thing to them, and so it would make sense that they can still operate in spite of fear. Remember, the Frightened Condition isn't just "you are sacred" it is generally "you are mystically terrified out of your mind". So, there is a lot of interesting space here for a race that is ALWAYS scared, so can still operate despite it.
2) Get a Cantrip. Solid ability, useful for all ages and ties into dragon magic.
3) A tail attack for 1d6+strength. I like and don't like this. I'd make it strength or dex, just like that more. Lizards and tail attacks are a perfect match, most of the most terrifying tails in the animal kingdom belong to lizards. However, I think I would go a step further and make the Kobold tail semi-prehensile. As trap makers and tinkers, having what would amount to a 3rd hand would be really interesting to play with. And I think that is more equal in power to their other options than a handaxe on their butt.
Then it plays into that Roar, with an ability that gives all allies advantage against all enemies within 10 ft of you. This is insanely good. This actually brings to mind a pack mentality far more than pack tactics ever did. They are signalling and communicating, distracting and becoming a target. This is AWESOME.
This might not fit the "traditional" view of Kobolds, but these guys are super interesting.
Feats
So, I'm not so sure about some of these.
Chromatic is awesome. Bonus action to get a non-concentration buff of 1d4 elemental damage to all attacks for a minute? Amazing. Add in some Absorb elements resistance and this is a solid feat, ready to go.
Metallic... that first ability sucks. 1/day Cure Wounds? I mean, this could be good for spellcasters who want those additional spell slots to cast it with, but... I don't like it. Their second ability though, is solidly good. Reaction +1d4 to AC to an adjacent ally? I like the visual, I like the ability, I might want to make it +1d6 instead, but it is decently good.
Gem is the only half feat, and I feel that alone speaks poorly for it. The reaction is nice, 2d8 and a push, solid, but I'd rather see something else than it being a half feat. And, it is one of those very passive abilities where you want to get hit but you probably put this on a caster who is going to avoid getting hit. Not a great ability.
Spells
/RANT
WIZARDS GET EVERYTHING AGAIN! WHY WHY WHY!
/END RANT
Seriously, that bugs me. Hitting these in order.
Draconic Transformation is likely balanced, but I don't think it feels like a Draconic Transformation. Compare to Crown of Stars which are seven 4d12 bonus action attacks with no Concentration. This is concentration with a bonus action AOEs of 3d8 force, see invisibility and flight. I think I do agree that getting an AC bonus feels appropriate here, but the damage calculations are likely balanced. Also worth noting, this is a Druid spell on top of the Sorcerer and -----
Fizban's Platinum shield... didn't impress me. Sure, it is good when facing things that cause dex saves vs elemental damage, but two of those elements are usually Con saves, and it can only protect one person, plus is Concentration. It could be good in the right situation, but how often would I take this instead of a different 6th level spell? I'm not sure. Only usable by Sorcerer and ----- to.
Flame Stride is really cool and really really powerful I think. Bonus Action for a +20 ft movement and you ignore opportunity attacks. You can only hit creatures once per turn by moving within 5 ft, for 1d6 damage, but that is almost gravy in a way. And, the creature has no defense against the damage, they just take it. Put this on a Ranger (who deserves it more than the Sorcerer and ------ Edit: Oh, artificers get this too. That is super thematic for them) who happens to be a wood elf? With Roving you could have a movement speed of 60 ft, and that is a lot of potential enemies to hit, especially if you use the DMG rules to allow movement through enemies.
Iceingdeath's Frost is also just a really solid spell. 30 ft cone of 3d8 damage and a grapple on any creature who fails. A grapple that requires an enemy action to break? Though, I just noticed, the range is listed as 15 ft, so their might be some debate there. I think 30 is fine, but maybe that would require lowering the damage. I just want a big "freeze" spell. Only Sorcerer and -----
Nathair's Mischief..... less impressed. 20 ft cube, random effect. Could be a charm, could be blind, could be incapacitated and random movement, could be difficult terrain. I'm not a fan of random effects, and this could be too may different things. They are all good debuffs, but hard to say if the spell will be useful in the moment. Bard, Sorcerer and -----
Raulithom's Psychic Lance. This spell is good, but I'm not sure why people are so impressed with the naming part. You hit a target you can see within 60 ft. They take 10d6 and are incapacitated (a lot of those effects going on) on an Intelligence save. Good, solid, straightforward. The Naming only allows you to hit a target who is behind cover or invisible. OH! I see now. The Naming also makes the spell FREE. No spell slot used. Holy breadbaskets that is good. Now, this isn't useful unless you have a 4th level slot (you still need to be able to start the casting) and it only works if you know their name, which is going to be rare, but.. dang, this is a death sentence if you know their name. 10d6 every round with no ability to take actions to retaliate? That is too good, perhaps. It is incredibly easy to shut that down, as a DM, but if the players work for it this kills anything that has trouble succeeding an Int save, and becomes a 10d6 cantrip. YIKES. And it can be used by Bards, Sorcerers, Warlocks, and -----
Summon Draconic Spirit is awesome. Just straight up. I know the breath weapon doesn't scale, but it also is at will. An at-will AOE of 2d6 in a 30 ft cone, of your choice of damage, plus two attacks of 1d6+9? That is a round by round 4d6+18, very solid. The spirit is going to have a great AC of 19, but is a bit squishy with 50 hp. Still a good amount of hp though. Plus, it is Fast and has reach. 80 ft fly speed and 10 ft reach means this baby is spending its time in the air while kiting the enemy, and it has Blindsight. Jeebus, this thing is monstrous.
Plus, pay attention to the phrasing of the breath weapon. It does a type that the dragon is resistant to, but they are resistant to 5 types. This means if you summon it to fight fire enemies, it has resistance to fire, but can deal cold or lightning damage, bypassing the common problem of "you can't hurt me, I can't hurt you" I'd rarely use the Gem version, since those are much less commonly resisted elements, and Acid will cut through most enemies who have elemental resistance.
Oh, and it gives you resistance.
Frankly, I think the Spirit ties that Psychic lance for most powerful spell on this list. Good for Druids, Sorcerers and ------, and as a Conjuration spell it can be buffed by Conjuration school or Shepherd. I want it, and I want it now.