It's true that "adventure" is a finicky term. Adventure games are things like Monkey Island, which have very little action-centered gameplay but are just called that historically because of Colossal Cave Adventure (1976). I'm just used to "adventure" in games meaning puzzles, inventory, a story, slow-paced contemplative gameplay, and sometimes no literal adventure at all. That's why Zeldas are generally specifically called action-adventures. But yeah, interactive fiction almost exclusively means text games, so "adventure" is a much better fit here.
Congratulations on the engine! I hear your about the asset creation. I work in Construct, which has its own graphic creation interface, and I struggle so much when I try to prototype in any engine that requires me to open a separate tool. Incidentally, I'm currently creating my own "engine" (really more like a template haha) for making very simple adventure games in Construct.
A separate button for the puzzle would've definitely ironed out the kinks in my experience specifically: I know I would've pressed the 4 relevant cells, hit the button, get the validation, and just assume the solution was pressing all the possible combinations of the symbols from the bottle. Then again, it would add a little more friction to the interaction, which not everyone prefers, so it's hard to tell. I do love it when apps on my phone validate a verification code just as I enter the last digit without asking me to hit enter (and extra points if they just recognize the code from the system clipboard).