On "Save As" MuseScore should add the score to "Open Recent"
MuseScore 3.5.2 MacOS
• New score
• Check the Open Recent menu: the score does not appear in Open Recent.
Nor does it appear when I close and reopen MuseScore
Here on the Mac I expect SaveAs to add the "saved" filename to the top of the Open Recent list.
I recently checked and that's how it works in other apps.