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 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 pair/update it for you.
Update;
With the announcement by Apple of ios16 and watchos9 later in the year,it was revealed that the minimum spec for these upgrades is Iphone8 and Apple Watch 4.
So the watch 3 will NOT be receiving those updates.