1. There should be a comment explaining that this is the name of the shared library on windows, perhaps also mentioning this link which seems to be the best source I could find on this.

Added a comment. Winsqlite seems to be kinda undocumented by MS, but it should be fine; they cannot just remove it without breaking compatibility.

I kept the code that tries to open sqlite3.dll first, because maybe someone was relying on this (and also I have no clue how sqlite3_flutter_libs works, and maybe that package needs that).

2. It would be convenient to test this as part of our CI.

I added a new dimension to the test matrix for system provided dlls vs the compiled ones.
There is some weirdness with winsqlite as you can maybe see in the commit messages.

The tests crash when trying to call the function to register a virtual file system. Atleast in CI. I cannot reproduce this on my Windows 11 machine locally.

For some reason either using --debug or enabling randomized test order made the regular test suite pass in CI. This doesn't work for the package with test helpers, so I ended up disabling that for winsqlite testing. I'm kind of out of my depth here.