My thoughts
Favored Soul
Certainly better designed than the last one, but I miss the access to melee capabilities. This one plays completely different than the last one. It fits the need for a charismatic priest, but it is not a favored Soul.
Divine Magic: Fixes one of the problems of the last version. It is powerful, but not OP considering the extreme limitation on sorcerer’s spells known.
Supernatural Resilience: Extra HP is always good, but the reason favored souls needed more HP was because they wanted to go melee. If you remove all armor and weapons, this become kind of pointless.
Favored by the Gods: Nothing to say about it. Mechanically is fine but it is not really flavorful neither fells necessary.
Blessed Countenance: Very powerful and with an interesting flavor. I like it.
Divine Purity: The only rotten apple in this archetype. It is mainly a highly ignorable ribbon. Make it only immunity to diseases and add something else. I want my wings back.
Unearthly Recovery: Nothing impressive but it does the job.
To make it more in line with the last version this is what I would do:
Remove Favored by the gods, add simple (maybe martial) weapons and light and medium armor (no shields). Blessed Countenance could turn back to Extra Attack or something that supports the use of GFB or BB, and Divine purity back to wings. I would not mind having two versions of a Divine Sorcerer. The Favored Soul from this UA with another name and an actual Favored Soul with melee capabilities.
Phoenix Sorcery
Interesting Flavor but bad mechanics. It is almost completely based on a once per long rest ability. And not even a powerful one.
Ignite: You can ignite flammable stuff. Like you can already do with fire bolt. Unless I am missing something, this ability is kind of pointless. It can stay as it is just a ribbon.
Mantle of Flame: Once per long rest you can fell to have a subclass. It must become at least once per short rest to be useful.
Phoenix Spark: Interesting and cool. But again only once per long rest. Now you can feel like having a subclass TWICE per day!
Nourishing Fire: Finally something at will. Interesting and powerful.
Form of the Phoenix: Very powerful and interesting, but again only once per day, and is not even a new once per day ability, it triggers together one you already have.
As I said above, the number of uses of Mantle of Flame must rise. And something at will needs to be added at level one so you can actually feel that you have a subclass before 14th.I also thinks that it should get fire resistance. Phoenix Spark is fine if the problems I said are solved. And Form of the Phoenix needs to be turned on only once per long rest if the number of uses of Mantle of Flame increases.
Sea Sorcery
I have nothing to add here. This is one I think could go directly to a book unchanged.
Stone Sorcery or earth Swordmage
My favorite from this pack. There is only one main problem here. Stone’s Edge is too powerful to be added to every cantrip. Make it only add a quarter your sorcerer’s level on cantrips or add nothing at all. The way it is it fells too powerful.
Other problem only appears with the AC bonus if you multiclass. But I don’t known how this could be addressed without removing it entirely. Level 6 is too far away to delay an important ability like that.