Just one addendum to this. Any M3 not factory specced with a tow bar will be 0kg towing rated, therefore won’t legally be allowed to tow, even if an aftermarket tow bar is fitted. However, that doesn’t stop someone from fitting an aftermarket tow bar and using a bike carrier on this (as long as it’s not one with wheels, as that’s technically towing). It’s still not great, though, as the car won’t have the 13 pin connector to control lights on the carrier. This is what the aftermarket kits you’ll have seen available are for.
If buying new, I would hold out for an M3 with a tow bar. I’ve heard these are available “off menu”, so if you call Tesla they might be able to match you to an inventory car (on a ship on its way from Shanghai) that has a tow bar. I think someone mentioned only LRs are available, at the moment, though?