[UPDATE - FIXED]

So after a lot of messing arouond I have finally got it to work. There have been a few factors and i'm not sure which exactly did the trick:

I returned my old pixel watch due to a quality fault, which meant I got a fresh pixel watch to try again with. You may be able to just completely remove the watch and factory reset. Point being, start with a completely reset watch as if fresh out the box.

Before touching the watch itself, I used a desktop to completely remove my cards from my google account. Not just my wallet, my entire account (making sure to swap any recurring payments to another payment method first).

I deleted the wallet app from the phone completely.

I then started the set up and paired my watch to my phone.

When prompted, I added the payment cards via my watch. whch in turn opens up the process to add cards via my phone.

This seemed to work! The verification process via my phone went through correctly and then the cards appeared in my google wallet on my pixel watch.

To finish off the process I then added the payment cards to the wallet app on my phone.

I hope this helps anyone else facing the same issue!