. . .I do find the talk that you can somehow recreate all these classes in 5e to be puzzling. I always found 5e to be staggeringly limiting and straitjacketing, a simplified version of D&D without a lot of options, one reason I have come to avoid it like the plague. My attempts at playing 5e were all "Here's the kind of character I'd like to play. . ." as I name off something I like from 3.5 (my preferred edition) to the DM, typically using some of the above classes, and I'm told point-blank that those classes don't exist in 5e and I should stick to the 12 classes, as written, in the PHB. After the 3rd separate group saying there was NOTHING like any of the above classes in 5e (each one saying there was explicitly no "divine sorcerer" like the Favored Soul/Mystic/Shugenja, since that's a favorite character type of mine), I rather took it to be the way 5e is played and written.
The reason you can't find a "divine sorcerer" is that the sorcerer and by extension the divine sorcerer is a mechanical hack that is almost entirely unnecessary in 5e because it's quietly dropped so-called Vancian Casting in favour of people getting spell slots. This gives the sorcerer itself identity issues (they made metamagic its "thing") and means that a divine sorcerer is just a cleric.
And to me that's a reflection of how overspecified and straightjacketed
3.5 is that you need an entire separate class to do something like the Favoured Soul when it has exactly the same spell list as a cleric and has very few non-casting class features; the only things you get before level 12 are from memory weapon focus and energy resistance 10. The Mystic is from memory little different, getting a domain rather than class features. These should not need to be separate classes and it's only due to how constraining 3.5 is that they are.
Almost everything you do with a Favoured Soul or Mystic is
exactly the same as you'd do with an ordinary cleric, and had you just described what you want to do and not been so hung up on the 3.5 names for classes you'd have been directed to a cleric - and found that the 5e cleric is in practice closer to the 3.5 Mystic or even Favoured Soul than to the 3.5 cleric.
Why would you need to make warlock its own class, if you could create things as completely different from other classes like artificer, favored soul, or archivist with the existing core classes. . .wouldn't warlock just be a variant of sorcerer then (since both are arcane casters that gets magic though means other than study)?
The thing is that a favoured soul
isn't different from a cleric in anything but their metagame mechanics that let them shuffle spell slots around. The archivist is little different to a cleric other than that they get a spellbook and fewer hit points. That should be a cleric domain rather than being an entirely separate class (cleric domains are far bigger and more expansive than 3.5)
The Artificer is a new class - and is a class in 5e. It just isn't a core class - and I agree with both decisions. The Artificer has a massive impact on worldbuilding because it defines both how magic items are made and what they are; this is something that different fantasy worlds should be allowed to vary and that 3.5 makes magic item creation a core player-side resource is yet another way it's overspecified.
And the Warlock? The warlock gets powers from their patron. They get a total of two spell slots before level 11 - but they recharge every short rest. They also get invocations that do not work at all in the same way as spells; their relationship to both magic and time is fundamentally different from a full caster. You can't do the same things at all.
tl;dr: You aren't finding what you are looking for because what you are looking for is something 3.5 doesn't offer you on the base classes but 5e does. So you're looking for something you only need because of how restrictive 3.5 is.
