The trick behind these roguelike mechanics is that typically you don't store much at all.
The shape/contents of each room are determined by an algorithm that's generally seeded with the position of the room, and possibly a unique key for each "new game" session.
This algorithm, which can take many forms, is effectively a deterministic machine: put the same numbers in, and you'll get the same room out. (But put in different numbers, and you'll get different rooms!) So you don't need to store the contents of the room to be able to re-draw it if the player doubles back. Just put the same position in again and you'll automatically get the same room.
This is how early roguelike and procedural games managed to pack such immense explorable worlds onto the tiny floppy drives and limited RAM of early PCs.
If the player can make changes to the rooms, then you do need to store those changes to be able to reproduce them faithfully. This storage generally grows linearly with play time, and can be discarded when the player hits a permadeath point, so even if it's conceptually unbounded it can usually be kept quite modest.
You can tune how much you need to store by the design of your mechanics: if the room repopulates whenever the player leaves it without clearing it entirely, then you only need a single bit of storage per room: a "cleared" flag. Or if the player's changes are limited to discrete cases: killed enemy/bombed breakable wall, you can similarly keep it scoped to some worst-case number of bits per visited room. Or you could have the player's changes "age out" after they move more than 10 rooms or 30 minutes' game time away, allowing complex state tracking with a limited time horizon. Games like Minecraft, which allow much deeper player customization of visited chunks, correspondingly have much more intense storage needs.
As for how "Unity" deals with this: it handles it however you tell it to. It doesn't have a built-in roguelike bullet hell component you're forced to use. So you can script whatever custom system you find will meet your game design/player experience goals and performance needs on your target hardware. Generating the next room's contents, discarding old rooms, storing what you deem important along the way, all of that is your responsibility.
If you ask a narrower question with details of a specific mechanic or piece of your generation strategy you'd like some help with, we can provide tailored answers about that particular problem.
