Use a VPN on the host and a VM with different browser and OS as guest that uses the host VPN network, so guest uses NAT. Create a snapshot of the VM and start browsing privately, don't login to any service or if you need to, with a fake identity.

When you're done with browsing, revert to the previous, clean snapshot to remove any track on the virtual disk.

You could even start another VPN on the guest, I use https://lnvpn.net/ to get a temporary VPN for a few sats.