> each "run" or playthrough you change the game state somehow (varies by game) so that the next run is easier / you have more in-game options for progression.
You've fallen for the hostile takeover. Roguelike used to mean the exact opposite of that: Each run starts from scratch, independent of all previous runs. Some roguelikes, that is, games like Rogue [0], implemented "player ghosts", monsters based on previously dead player characters, but that's the only persistent progression in a roguelike.
It saddens me that the term has been hijacked by modern indie developers to pretend to mean just about any game that has any amount of randomness in it. Dead Cells is not a roguelike. Hades is not a roguelike. They are action RPGs more like Diablo. Diablo, by the way, is also not a roguelike.
WHAT IS A ROGUELIKE?
As the name suggests, it is a game like Rogue. The genre hasn't evolved a better name yet, kind of how first-person shooters were originally called "Doom clones". So what was Rogue like? First and foremost it was a turn-based tactics game, where you had an unbounded amount of time to ponder your next move. It had highly randomized content, you'd have to make do with what you found. It was a dungeon crawling, exploration, turn-based tactical combat game with permadeath and no persistence of progression. You lose, you start all over.
[0] https://en.wikipedia.org/wiki/Rogue_(video_game)