I don't as there is a service called blik in my country which seems private enough and is way more hassle free to use. It generates one time use codes for payment and requires user confirmation for each payment. Not sure how private it is on the back end, but it pretty much gets rid of the same risks virtual credit cards target. It's also pretty well supported, both by banks and payment processors.

Again not sure how private it is on the back end, but, at least for me, its more user friendly than using a credit card so I cant be bothered.

Edit: the privacy policy for both blik and their website (I think?) is 13 pages, 9 of which give a detailed description of how they use cookies. Also the privacy regulations here are quite strict and they actually follow them, so you can not opt into cookies with as much effort as it takes to opt in. It is also a service made by banks, so I feel its quite trust wordy.

Also OP, if the banks web extention doesn't require access to all websites, it probably won't track you, at least more than your bank tracks you already.