Payment leaves a huge identification trail because of all the know your customer stuff these days.

If they accept monero or something then ok but I doubt they will.

They could make it so all that is known by banks is that you purchased the service. Like how Nym does it or how you can buy Mullvad credits on Amazon.

https://nym.com/zk-nyms

Ideally they accept Monero and do unlinkable payments but I doubt they will accept Monero. Hopefully they accept some crypto.