NOTE: This is just my five cents, please correct me if I am wrong.
I'm pretty sure it doesn't matter, because in the end, you'll be browsing through the same IP endpoint, since the connection to the carrier will get allocated the same public IP regardless of which device the SIM card is inserted to, thus the carrier can track you through that.
But, for your threat-model, all this wouldn't matter anyway, because Google & friends cannot easily track your cellular usage. Unless you're using Google Fi, of course.
I'd actually recommend you use it on your GrapheneOS device, because I am pretty sure less sensitive permanent identifiers get leaked to the carrier, thus improving your privacy.
So, to summarise, the privacy benefits are basically none and, most importantly, you likely just make it harder for yourself, because you now have to phones to keep up-to-date and maintain and keep secured (remember, there's no privacy without security).
Good luck!