Where does the indication of unavailable or available (loaded) projects / websites is saved?
I have a solution which has some unloaded projects while only the website is loaded
Of course I can right click and reload it but still, I want to now where this [unavailable or available] info is saved?

I’ve been looking in the sln, there is no difference (beyond compare) between loaded one and unloaded one.
Also in Websites.xml, there is no such difference
The suo file stands for “solution user object” (it’s a guess).
It’s a per-user container of solution settings.
You can safely delete it, but you will lose some other non important things, like breakpoints, and so on.
In most VCS, this file is in the standard exclusion list, as it should remain specific for each user. This is the evidence you can safely delete it.