I played a Halfling Barbarian in 3.5, albeit only briefly. The dino-buddy was a mount; a bit of an NPC ally; nothing with the complexity or growth of a Druid or Ranger pet but still there. I could see a similar thing working with 5e.
For example, how would you implement that Talenta Halfling Dino Riders? Halfling Barbarians could work, but they are missing that thing that really implements or emphasizes that bond between themselves and their dinosaur companions. Halfling Beast Master Rangers might work, but the mechanics of the ranger don't necessarily fit with the concept. So I created a Barbarian archetype to better match that concept. I'd like to see more archetypes that can better align with the character concepts that have been presented in Eberron. Perhaps a Sorcerer Dragonmark Bloodline that could parallel the Dragonmark Heir and allow those rare Siberys marks to manifest. That would be cool! And other things like that.
Based on what I saw in Races of Eberron, a good number of the tribal halflings with class levels are rangers or rogues, so I can see where that might come from. But from reading the ECS, their culture seems more along the lines of barbarian halflings, especially since the leading of one of the largest nomadic tribes, Lathon Halpum, is a barbarian, that is the flavor I drew from for inspiration. Also, the idea of halfling barbarians (something not normally associated with the smaller races) appealed to me.
Not saying it couldn't work like that. It's a fine way of handling it. But as I said before, I like making homebrew mechanics that can work to reflect and assist the character concept. Not saying it always has to be done that way, but it's a nice bonus.
The biggest suggestion I have here is don't worry about having mechanics to represent everything. You don't need mechanics to say that they have a special bond with their mounts. But if you really must, just say that they're especially well trained and give the rider advantage on all animal handling and loyalty checks. You could even make a special Talenta background available to halflings only that mimics the outlander, but the special ability is advantage on specific rolls dealing with their mounts and others of their culture.
If you really want dragonmarks like they were in 3E, just import them directly and correct the pieces that don't work. 5e characters don't get a feat at first level, but that's easy enough to say that every PC get's a free feat at lvl 1 for your game and poof, just like 3E Eberron if I recall correctly.
Class =/= Culture. I can't emphasize this enough. The barbarian class is not the barbarian culture. The outlander background best represents the barbarian culture and backgrounds do a lot more to shape a characters outlook on the world than class does. I can make an acolyte barbarian and he's a religious zealot who flys into a rage, or a mage apprentice (don't remember the name of that background) barbarian who quaffs special potions to instill his rage, etc. Having an outlander fighter, ranger, rogue, barbarian, cleric, whatever is so much more appropriate for the barbarian culture than to pigeon hole everyone who lives off the land as the barbarian class.
If you really want to make homebrew mechanics for everything, I wish you the best of luck. I'd rather just wing it to get the feel of the setting than fret over mechanics and how/if they are balanced or fair.
I never said class equals culture. In 3E Eberron, most people don't even have class levels outside commoner or adept, so you don't even need to make the assumption that Talenta Barbarians are mechanically barbarians. And as I said before based on what's presented in the Races of Eberron book, most Talenta Halflings with class levels are rangers or rogues. But also, as I mentioned previously, in the ECS the described leader of the Talenta Halflings is statted out as a 9th level barbarian. It's right there in the entry on the Talenta Plains. This leader was known for his prowess as a battle rider. If you wanted to play a character like him, how would you go about it? Sure, you can just give him the outlander background, maybe just give him a generic dinosaur as a mount, or make him a beast master ranger.
Barbarian with the Mounted Combat feat? Plus most beasts that work as mounts have some rules in the MM explaining any special rules they might have in relation to a rider. I would imagine that its not too hard to come up a few rules regarding deinonychus and charge attacks while used as amount.

Here's a question: in terms of new content for Eberron in 5e, are people more interested in crunch (player options & adventures) or fluff (mini-setting books and... well, adventures too, depending)? Yeah there's two campaign guides and quite a few fluff books from 3.5 but there's a lot to the setting that haven't really been explored in great detail (planes, undersea, etc.) Curious what people would most be looking forward to if official support (either WOTC-produced content or DM's Guild opening) ever materialized.
Firstly let me say it’s great to see someone generating conversation about Eberron. It’s my favorite setting by far and sadly neglected.
To answer your question, for what its worth I most treasure ideas on (a) Eberron specific adventures and plots or (b) converting generic or other-setting 5E material into the Eberron setting/themes. There's so many hooks in the setting it's a tragedy that WoTC haven't provided more support.
Regardless, thanks for keeping the flame alight. ��
Here's a question: in terms of new content for Eberron in 5e, are people more interested in crunch (player options & adventures) or fluff (mini-setting books and... well, adventures too, depending)? Yeah there's two campaign guides and quite a few fluff books from 3.5 but there's a lot to the setting that haven't really been explored in great detail (planes, undersea, etc.) Curious what people would most be looking forward to if official support (either WOTC-produced content or DM's Guild opening) ever materialized.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.