Let's say I'm playing as Seoni and I'm down to my last 6 cards but I'm sitting at the Thassilonian Dungeon location. If I play a spell from my hand, which is then recharged automatically in this case (or I'm some other character and successfully recharge the spell) would I then immediately draw that spell back into my hand based on the location's ability?
No. The location effect triggers immediately when you play the spell. But the spell isn't in your draw pile when you play it. It is waiting to see if you succeed at the check to recharge it. This is more obvious during an encounter.
Apply any effects that happen when you encounter a card.
Apply any evasion effects.
Apply any effects that happen before you act.
Attempt the check. You play the spell here. You also get to draw a card here.
Attempt the next check, if needed. You would attempt to recharge the card here. Seoni automatically succeeds, but either way, the card doesn't go to your recharge pile until this step. But you drew a card on the previous step.
Apply any effects that happen after you act.
Resolve the encounter.
Even outside of an encounter, the same would be true. If, after playing the spell, you attempt the recharge check, it is no longer "when you played" the spell. And it definitely isn't immediately. So, the answer is no, because you haven't recharged the spell at the time you played it. It goes Play/Draw/Recharge.
If you could, Seoni could use a Scrying spell over and over, for instance. This can still be achieved if you have two copies with one in your hand and one as the last card in your deck. It would be a dangerous game to play though. And kinda boring for the other players.