barbarian: rouser of armies, generally killing people, temper -> Rages when fighting, TOA specific - killing Commodus 2 times in the way he did. as a multi-class thing, Apollo getting pissed mid battle, flying into a rage and suddenly fighting with his sword / bare hands. Learning to control and wield his rage to suit him and his allies in a useful destructive way!
bard: God of Music. And dance. And many more. Yeah you know this one.
cleric: bridge between divinity (Zeus & the fates, etc) and mortals, performs miracles and heals people, spreads his name & faith in the gods in the many places he goes, identity as a good, caring, involved father of his children -> patient and loving towards people he helps with added godly miracles.
druid: associated with hunting & Artemis, possibly was a hunting god in Archaic period(?), associated with a lot of animals which he also turns into (dolphins in the Homeric hymn come to mind). In order to build cities, you need to have good knowledge of living and working with your physical environment and surrounding as well as generally be good at surviving and thriving in the wild.
fighter: he fights?? Good with a sword, bow & arrow, fisticuffs - could be translated into a decent range of weapon proficiencies. Maybe he’s a fighter with a LOT of hobbies?? You could also throw him being a teacher in here - maybe he teaches fighting to kids??
monk: good at wrestling? Beat Ares at wrestling in the Olympics, Wrestled Phorbas and killed him. Similar to the barbarian anger thing, but less finding a useful outlet for anger and more controlling it and calming yourself. TOA specific - Commodus again.
paladin: upholds faith in the gods, delivers vengeance for them (when hubris’d) & (forcefully) protects devotees of the gods (I guess most examples are of his own eg. killing Neoptolemus when protecting his priests, etc.), and punishes hubris (could be more specific to the gods)
ranger: good with a bow & arrow. Associated with wolves & ravens. Hunter. Associated with Artemis.
rogue: the Odyssey mentions him (and Artemis) being the reason for sudden death because of their arrows - they’re silent, deadly, and unpredictable. Also something something intense light creates shadows. Could lead to an Apollo & Artemis tag team!
sorcerer: Divine prince of Olympus & favourite son of Zeus has GOT to have inherited power from his parentage. Very much the ‘extremely powerful son with the gift of prophecy whom the land itself tried to prevent from being born but was anyway’. Also a lot of exploration on his own heritage & inheritance - you could explore Trojan Apollo practicing his magic as a way of maintaining Trojan culture and his own heritage that is now almost gone. You could also mess with the many different theoretical origins irl Apollo has and make WHAT he inherited his power from a mystery.
warlock: ok this one is hard. perhaps myths where Apollo inherits / takes domains in a dodgy way. Particularly i think in terms of his associations with beings that aren’t quite gods / divine / worshipped per se, but are gods / divine / worshipped in a culture that an Apollo-worshipping culture then invaded / build relations with, then becoming their warlock out of repentance / power shifts depending on what the religion of said area would actually look like (maybe he’s introduced as a warlock of that divinity who then becomes more powerful and more worshipped by the people, then overthrows said divinity / breaks their pact) out of technicalities would be sick. For instance, Apollo being cursed to be a warlock of Python / Gaia to slowly inherit Python’s power, guided by his/her undying corpse is a pretty cool concept. Alternatively, being a warlock of Daphne out of remorse for what he did and her making sure he now protects people wherever he can & is a force for good, wearing laurels as a symbol of his pact!
wizard: god of knowledge etc etc. I see no reason why his desire for knowledge stops at learning how to manually shape the world around him! He can have whatever stone the Hyacinth one is as part of his staff.
artificer: he made the kithara and also something something cures eye injuries - he made tools to do so?? Again lots of pushing and pulling with this one, maybe crafting medicines could arguably count. Um he built Artemis’ first temple out of bones and goat heads (I think? Goat something) in that one account of a myth. I could see him having a phase of getting into making things himself.
blood hunter: blood sacrifice. The purification rites of Orestes & himself (after slaying Python), the Lycanthropy, the Odysseus dedicating his slaughter of the suitors to him, etc. He deals with a lot of moderation WHICH WOULD TRANSLATE TO SACRIFICING ENOUGH BLOOD TO REAP THE BENEFITS OF PERFORMING MAGIC WHILST NOT SERIOUSLY INJURING YOURSELF, NOT IMPLYING THAT HAVING ‘A LOT OF’ BLOOD (WHATEVER THAT COULD EVER POSSIBLY MEAN) IS BEING EXCESS FGFHNDHDNFN