Fingerprinting works by collecting bits of information about the browser and device to identify users. Couldn’t browsers like Firefox see when a website gets such info with JS and either prevent or ask permission from the user for the website to make HTTP requests to upload such information to the website. Idk if they do something like this already.
https://support.mozilla.org/en-US/kb/firefox-protection-against-fingerprinting
Firefox also has a resist fingerprinting setting, but it can break many things.
If it is really a concern, I have heard the mullvad browser essentially the tor browser without tor.
I think in regards specifically to the question of resolution, that anti-fingerprint setting will start your browser at a smaller, set resolution. The problem is nothing prevents you from just expanding the window, so it’s not a very strong solution in that aspect.
It usually expands in specific increments, so you still end up with a common size.