Apple watch showing full green screen

You might want to wipe it clean and start all over again.

What to do before you sell, give away, or trade in your Apple Watch, or buy one from someone else - Apple Support

Don't load the backup. It will be a minor PIA reconfiguring the watch but the data is safe (it's duplicated in the iPhone).

Set up and pair Apple Watch with iPhone - Apple Support

You mention the word “small” and that is the reason an Apple Watch can’t be repaired outside Apple’s central repair facility. Everything is miniature, it is integrated onto one circuit board and just too small for field repair so Apple has determined the only practical solution is a service exchange device. Your watch is out of warranty so you have to accept the standard non-warranty exchange pricing.

That is the reality of ultra compact electronics.

It is pointless to be disappointed. I suspect there may be only one or two service facilities worldwide which are certified to handle full reconditioning for a defective Apple Watch, including renewal of water resistance to make the reconditioned device “like new”. If that level of cover is what Apple has determined to be adequate and economic to maintain we can’t argue with their informed decision, and it does allow proper control over quality of work which would be almost impossible with dozens of facilities spread around the world.

Oh... and even if you lived in the same street as the repair facility you would still get the same answer in your local Apple Store.

You need to call Apple support to assist you further