Why not just make another google account that you solely use for registration in services like these? Use a virtual machine with VPN if you really do not want it to be linked with your real account.
It is a bit of extra work but that's just how it is nowadays.
Does not google require a telephone number to create accounts nowadays? In some regions there are no anonymous SIM cards by law. (Temporary number services may not work well.)
There do exist anonymous credit cards, paid with cash, for fixed relatively small amounts (e.g. ~100u. In Europe there are restrictions to these kind of payment methods - cards must be below, I believe, 150€).
It is very much possible to create temporary credit cards linked to your real bank account for one-off purchases. Apple Card provides that as a service (US only) and other countries have similar systems that every bank adheres to.
Plus, you may not mind not being anonymous to Midjourney but mind not being anonymous to some other service (like Google).
It is a bit of extra work but that's just how it is nowadays.