How can I pair my Apple Watch series 1 to my phone when my watch says it is a valid Apple ID?

It's technically possible to pair a watch 1 or 2 to a newer phone,but in reality this is proving almost impossible for just about all the 1&2 owners on this forum.

Newer phone's require the watch to have updated hardware to cope with ios 14 or 15 and unfortunately because of the age of these watches the hardware is very limited to what it can do.

Then there is the subject of storage,these watches have very little storage space and the average software update now requires gigabytes of space rather than megabytes and again these watches are very limited with the amount of storage space they have.

It is recommended that even a watch 3 should be unpaired and repaired in order to free up enough space to update.

And;

You can ask apple to remove the activation lock online on this page;

Online Activation Lock Removal Tool.

Or this;

If you can't remember/gain access to the apple id that paired the watch to the phone.Take the watch and it's receipt along with some photo id and any other proof of ownership to an Apple Store and request that they remove the Activation Lock for you.

You will need to remove the watch from the Apple ID was set up with. If you don't know the Apple ID, you can ask Apple for help, BUT and this is important, you will have to prove you are the original owner of the watch, by presenting the original purchase receipt to Apple with the serial number of the watch on the receipt. Whether you have that after all these years, only you would know. You'll also find a Series 1 watch is now VERY out of date and the effort required to be able to use it may not be worth it. That's up to you however.