Yeah I was already doing what you said, so that at least confirms I wasn't playing the game "wrong".
I learned that the problems only occur when using keyboard controls. If I use mouse clicks on the HUD, the game seems to work as intended and it is in fact turnbased. With keyboard input, it seems like turns are handled immediately while I hold the key down without any grace period, which results in adjacent enemies attacking repeatedly every few frames. I thought the game was real-time because of this, but now that I know it's turn-based, it's playable :D I just can't use any keyboard controls. For reference, my specs are win10, AMD R7 3700x and an Nvidia 2070S.
I'll give it a proper go tonight and will update my comments!