Banks will often block VPNs and Tor, or at least it’ll be a red flag for them if you try using one. If you never want to leak your true IP, you could consider self-hosting a VPN on a VPS or maybe use Windscribe’s residential static IPs. But your ISP and bank are already tied to your identity so I don’t see much benefit in trying to obfuscate your true IP address from your bank.
The Tor Browser is the most private browser whereas Mullvad Browser is virtually the same thing minus Tor. Many people still choose to use other recommended browsers instead, any of them are fine for personal use like banking. As for social media, the Tor Browser is always going to be the most anonymous but they will often block Tor users or at the very least require you provide a phone number.
You can try purchasing a VoIP number anonymously but some platforms might detect and block sign-ups from VoIP numbers, so you’d have to either pay more for a “real” (but internet-accessible) number or purchase a burner phone with a pre-paid plan in cash.
If all of this sounds too complicated, just use Brave (or Firefox if you wanna stick it to big tech) and don’t think much more about it.