My understanding was that privacy.com is just a “detached service” implementation of something that many European banks offer natively as a feature of having a credit card (or even just a chequing account) with them; and that privacy.com was only viable as a business because, for some reason, American banks are (or were at the time) totally unwilling to build anything like this, so people were willing to settle for a (strictly worse from a “privacy” perspective) third-party-MITM-proxy card if it meant having this feature.
I’d suggest, rather than looking for a “detached service” that does this, look at what (probably larger) European banks besides than your own offer their customers built-in.
My Indian Bank, HDFC offers this since 2008, virtual cards with custom amount, one time use. On creation, the amount equal to limit gets set aside. If merchant charges less than max limit, the excess comes back.
Thier at-time debit cards were good only for domestic transactions, but this virtual was good for international, & used to come up as Visa Prepaid. I used it for registering domains & amazon international shopping.
I’d suggest, rather than looking for a “detached service” that does this, look at what (probably larger) European banks besides than your own offer their customers built-in.