I’m not sure about Monster Tain but Slay the Spire is not a roguelite, it’s a proper roguelike. The key distinguishing factor is that the meta-game progression doesn’t make the game easier, it just makes more of the content available. A fully unlocked StS on ascension 20 is much more difficult than the starting game.
The original roguelite was Rogue Legacy which started you with a weak character and allowed you to get stronger through multiple runs and deaths. By the end you had a very powerful character which made it much easier to win. This is the essence of roguelite gameplay: metagame progression that reduces the difficulty and rewards repeated play, helping you to win the game without having to master it.
IMO Enter the gungeon did the metaprogression without making your character stronger part really really well, would hugely recommend trying it out if you haven't and don't mind it being real time.
The original roguelite was Rogue Legacy which started you with a weak character and allowed you to get stronger through multiple runs and deaths. By the end you had a very powerful character which made it much easier to win. This is the essence of roguelite gameplay: metagame progression that reduces the difficulty and rewards repeated play, helping you to win the game without having to master it.