Solution for anyone who has this problem.
I switched to Vodafone, and a brand new number, from O2 last week and was setting it up on all of my Two Factor Authentications and the automated confirmation codes were all coming through apart from PayPal's.
The Pixel has a Spam & Blocked folder and none of these texts were appearing in there either, so there was zero indication it was anything on my end. My old phone on O2 was receiving the texts, as well as a brand new Sky Mobile number, but not mine.
After a few solid days of talking to Vodafone, PayPal and the bank (something to do with a "Safe Device" that popped up on Google) and going over the same things, I eventually just tried adding the 67975 number as a contact.
This is where I saw the red text that said "Blocked" underneath it. I unblocked it and tried sending the PayPal confirmation code again and it came through instantly.
If this is Pixel specific or not I do not know, but it was the only number that appeared to be blocked by default. I was never told to try this method, be it by the help teams or looking it all up on Google, so I made an account on here to write a post for anyone that has this issue in the future.