Aaaah I spoke too fast. There's an issue with GOS and Phoenix. I've emailed them and here's what they've said:

"> My plan is to use Phoenix on my GrapheneOS profile that I use the most so I'll keep it online all the time.

Keeping it online isn't enough, as we have no way to automatically wake up the app on Graphene. So even if the phone is online, Phoenix might not be. Btw we will have the same issue when trying to pay the refund invoice: we need to synchronize with you so phoenix is up and connected when we make the payment. These limitations really degrade the UX.

Best,

Phoenix Support"