Lightroom will oragnize them on input if you want, and follow any structure you assign. I have it store them in the way you describe, and it’s one of the reasons I haven’t moved off it, despite still using LR Classic.
FWIW, if you just want a one time extract from Photos, $10 for a month of LR might be worth it. If you’re looking for other options for longer term DAM/Editing features, there was a thread on here last year discussions LR alternatives (some of which were mentioned, eq CaptureOne).