It’s not so much a Windows vs Linux thing, but rather that the two styles say where to look for the libraries. The quotes-style says to look in the local directory while angle-bracket-style says to check the system’s header path.
The big benefit to the “quotes-style” is that if no local files are found, most compilers then search the system path as well.
I don’t know why SDL3/SDL.h has switched to angle-brackets-style includes, but you can edit your project include directory setting to include your local SDL header and dll directories. (Please follow steps 4-9 in the lazyfoo link). I think this will fix the issue.
Apple frameworks want to be included this way: brackets, not quotes, a framework name as an explicit directory. It was easier to stop fighting it in SDL3.