Using Mullvad Browser + Mullvad VPN could mitigate this a little bit. Because if you use it as intended (don’t modify Mullvad browser after installation) , all Mullvad users would have the same browser fingerprint and IPs from the same pool.
The problem is it's all or nothing. You must foil IP address, fingerprint, and cookies - all three at once.
Mullvad browser might make your fingerprint look similar to other users, but it's not common is the problem. Test it with the EFF Cover your tracks site.
Mullvad, (the vpn, I have not tried the browser) uses a single account number as both name and password, no emails. It allows for multiple anonymous payment methods and it's open source.