My Apple Watch is stuck on a boot loop blinking just the Apple logo when connected to the charge or just showing the Apple logo and going off when not connected to charge. The iPhone it was initially paired to got stolen. How do I restore my watch?

If your watch was repaired by Apple Service or an official approved service center I suggest get it back to them as a failed service (complaint) because it never worked to re-pair to your iPhone after the service. If you tried to do it yourself, or an unapproved workshop, then all bets are off and we might not be able to help you.

Your description with the logo cycling repeatedly when on charger power, and going to black screen when off charger suggests the battery is almost completely discharged and does not have enough energy to complete the startup sequence. The charger alone does not have enough output to power the watch through a reboot, it needs the battery. Try leaving it on charge for several hours, and if possible overnight.