To know how to manage things write in paper what things the map needs to know, what the levels need to know, and try organize, could be on files, using a general manager, using the maps as managers...
But paper and pen will be always your best friends.
Now more on topic.
In the case of SMB3, it has a persistent UI at the bottom, then the map and the levels on the same space...
I can think of:
When enter a level, remove MAP of the tree and store in a variable, global or in UI or a utility node, then load the level.
|-PLAYER (or inside tilemap?)
When exit level save something in a file/variable like if has special unique items, also if finished, and delete the level, then reenter MAP to the tree, updating changes (unlocking paths, change level icon status).
Don't forget to abuse the capacity of Godot to make super quick prototypes and try all the crazy ideas you have without overthinking, in some proptotypes you may get some cool partial solutions that can be turned into scenes to use/merge later.