Can an extension installed on Firefox access data from another browser, say Chrome?

Forgive my lack of understanding with regards to browsers. I am just starting my journey learning to code and I am setting up a live server extension to practise html.

I am a bit distrustful of using extensions considering the high level of access that they have to read/write and access data on a browser. The browser I use for my personal stuff (emails, accounts, youtube etc) has no extensions except for adblocker. I have a blank vanilla version of another browser (firefox) for using live server and any other possible extensions that i may need in the future.

My question is whether or not this one browser with extensions that can access & or read/write data has the same priviledges across to my other browsers. Is it solely the browser that the extension is installed on or can they ‘cross communicate/see’ another browsers webpage data?

Maybe I’m being overly paranoid but I would like to keep the browser that I use for my personal stuff secure and not compromise it with an extension. I am also aware that you shouldn’t just download any extension and should be certain that you trust it before installing it.