I don't recognise that item from an F4 (at least not from an OEM part from an F4).
Some explanations are:
Is it possible that it stuck to your tyre and and may have fallen there once the tyre cooled?
You may have just parked your bike over it
During a ride it may have flicked up into the lower fairing and fallen there when you put the bike onto the side stand
It may have been moved under the bike by being kicked
I only give these as examples as, again, I don't think it is from your bike.
Looks like a bolt spacer either raising something off something or a spacer within to separate a bolt from the sidewall. It could be a bushing around a bolt but they tend to be brass. Check your side panels for any loose areas.
I'm fixing what the previous owner and or used bike dealer f'ked up. It might be a bit of FOD that had fallen into the frame from somewhere and just now dropped onto the garage floor. It's not a whatsit that I had previously removed.
Just being careful.
I swear that every bleeping visible screw on the bike was loose, the ones that aren't loose are missing. LOL
This might also have been off an old 900SS and found its way out of the bolt collection just to bug me. (sigh)
Just label the misc parts and bin them. Once you work your way around the bike you'll most likely be better informed. There are spots on top of the engine where extra hardware can rest. Keep your camera handy while exploring fixes.
Metal bounces and rolls away when it hits the floor ESPECIALLY a round piece of metal. Then it grows legs and finds it's home in the one place you would never find it! I find it very unlikely that it's from your bike...unless your floor is sloped in all directions towards your bikes gravitational center haha.