JimH I don't think it's appropriate for me to tell you what you should do, but I personally logged in to my phone when it had Stock on it using my regular Google account. A few minutes later I flashed GrapheneOS and logged right back into the same account.
I don't think it really matters. The hardware IDs that they can access while running Stock are no longer accessible by them with GrapheneOS. You can use a completely new account and they won't know it's you (unless you give them identifying info, of course). Or don't use Google apps at all if you choose.
Google having hardware IDs is nothing in comparison to the amount of info they can access on a phone running Stock. I would focus less on the hardware identifiers and more on the data they have access to, which can be very limited on GrapheneOS.
I'd suggest reading through the section on hardware identifiers and the following section on non-hardware identifiers on the website.