The game autosaves at the beginning of every encounter I think. I know I've been able to quit a game and resume right where I left off

The game autosaves, so you can never load anywhere else than where you just left off. Any mistakes/deaths are permanent until the next run.

If you want to save scum just backup the save file.

"\Steam\steamapps\common\SlayTheSpire\saves"

Alt+f4 and the built in functionality "save and exit" does the same thing. If you load the save, you start at the beginning of the match. The card draw is the same though, so you will not magically beat the boss if you are using a unsuited deck.

A friend told me all of the above by the way, I play super fair. Never save scums at all. Nope. Nunca. Never happens....

Why doesn't it save when you get back to the map screen? It's generally a good place to quit. I've quit from the map screen several times and every time I load back, I'm presented with the choice from the end of the previous battle which I already made at the end of my previous session.