Fingerprinting unfortunately uses more than useragent strings. It takes hashes of data in your browser from a javascript context that is not easily masked or removed. For example, it might render a gradient of colors projected onto a curved 3d plane. The specific result of this will create a unique hash for your GPU. They can also approximate your geolocation by abusing the time-to-live information within a TCP packet, which is something you can't control on the clientside at all. If you TRULY want to avoid tracking by google, you need to block google domains in your hosts file and maybe consider disabling javascript on all sites by default until you trust them. Also don't use google.
How must it feel being clever enough to come up with these ideas and then implement them for companies invading everyones privacy for advertisement revenue and malicious information serving or stealing.
I guess they sleep soundly on a fat bank account.
Jokes aside, keep in mind that the idea of fingerprinting is that your computer's configuration is as unique as a fingerprint (e.g., your monitor is x resolution, you are on this operating system, you are using these following extensions in this browser, you have these fonts on your system).
Setting your user agent to something super unique is basically shining a spotlight on yourself.
I have a novice coding question using the mouse tracking as an example: Is it possible to intercept and replace mouse tracking data with generic inputs? For example, could you implement an overlay that blocks mouse interactions, and instead of physically clicking on elements, send a direct packet to the application to simulate selecting those elements?
Yes, it's possible. That's the way a lot of automated web UI testing tools work. The problem with doing it during normal browser use is that your intentional actions with the real mouse wouldn't work right, or the page would start acting like you clicked on things you didn't click on.