I am making a game that procedurally generates a level and sets tiles via Tilemap.SetTile().
I've been reading and watching tutorials about saving in unity and from what I understand I need to serialize data so it can be saved in a binary file. However, I don't even know where the data about the tiles in the tilemap is being saved.
How could I make this system - where can I find information about stored tiles in a tilemap?
Is there perhaps an already finished saving system that supports Unity tilemaps on the Asset Store?
As already mentioned in a comment, the "serialization" in Unity is absolutely garbage - completely forget about it.
All you do is save the info, probably as JSON, just a text file.
Note that the Json helpers built in to Unity are completely perfect - very easy to use.
Here's a simple and famous example ... https://stackoverflow.com/a/40097623/294884
(Note that you don't literally have to use Json, you can use any simple text format, but Json is so easy you may as well use it.)
There are actually dozens of QA on this site where someone asks "I want to save _ _ _ in Unity, how do I use serialization?" in every single casethe answer is just "Unity serialization is a joke, just save as a text file."