I want to start a new 2D top-down project in Unity and want to figure out how to organize my background (one big file or a lot of files joined together).
So how big can a background file get in Unity?
The target platform is Windows.
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Since it is for your actual world, you want to go by tiles. That means you have a sprite sheet and build your world of multiple of small pieces by it.
There are a lot of tutorial on how to build them out there, the documentation has a few examples as well (https://docs.unity3d.com/Manual/class-Tilemap.html) and for prototyping you can find a lot of free assets out there as well.
Usually a tile is 16x16, 32x32 or 64x64px per tile, bigger would be highly unusual and impractical.
A tile map sheet (multiple of your tiles), are packed together in one file and they can get as big as needed, though normally you don't want to have tiles in it that you dont actually use in your level.
In case you want to create a realistic street network as from your screen shot link, check out this good answer How to generate a city street network?
Since your city is static, you will get the best result if you handcraft it with segments. Compared to using one big image for all streets, it will make it easier to fit your buildings in or if you want to change later part of the streets. You can still use tiles for most of the straight and curves (which will speed up your building process a lot). For more complex curves you might want to take a look at splines.