In particular, I like the part where you build your deck from a set of themed sub-decks before the start, and then it's up to you to find the synergies between those themes. Not sure if there's an existing term for that mechanic. I think it may count as a form of a deckbuilder, but editing the deck's contents isn't part of the main game loop. Maybe a deck drafter?
I also like that it's a compact card game that doesn't take long to learn or play, and plays well with only 2 players. The only other drafting games I've found have a board, lots of pieces, and are aimed at 4+ players.
Trying to search for games like Compile is a bit difficult, because in the other threads I find, people like to focus on the lane battling aspect, which I could take or leave. I'm mostly interested in compact drafting games for 2p. Anyone know any?
I haven't tried Compile, but your description reminds me of Sorcerer from Wise Wizard Games. It is similar to what you described. As part of setup, each player picks a character, domain, and lineage deck and shuffles the three together to get a deck to play a tactical card game.
The game itself is fun. You always have options for what to do on your turn but never enough actions to do everything. The deck modules each have a distinct identity and abilities, creating satisfying asymmetry.
I did run across Sorcerer yesterday during my searching. I think the only downside is that it doesn't look very compact. But I am intrigued, thanks for mentioning it.