I can’t pair my series 3 watch without completing an update, please help

Perhaps these articles will help:

If you see 'Unable to Verify Update' when updating Apple Watch - Apple Support

Connect to Wi-Fi on your iPhone, iPad, or iPod touch - Apple Support

If your iPhone, iPad, or iPod touch won't connect to a Wi-Fi network - Apple Support

The apple watch 3 GPS only has only 8GB of internal storage, most of that is taken

up by the operating system and other critical software with not much space left for the

update.So installing or even pairing to an ios14 or ios15 phone is proving nearly

impossible for just about all the watch 3 users on this forum.

same applies to Apple watch 1 and 2 they are almost impossible to either pair or

update with an ios 14 or ios15 phone.

Your best course of action is to call in at an apple store and ask them to update it for you.