I need a browser that allows me to run multiple tabs or instances, but I need that each page is completely isolated.
So I should be able to use a different proxy on each page and separate cookie store and cache.
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Oni, Ghost Browser lets you isolate browsing Sessions in each tab. You can also assign a different proxy for each tab with new Ghost Proxy Control extension. No messing VMs or anything. Everything is right there in one browser window. More details here: https://ghostbrowser.com/blog/set-different-proxy-for-each-tab/
Thinking out of the box and back in the best that I know of is to use Virtual Box or VMWare to run multiple operating system instances, each with a browser running, possibly "full screen", in tabs.
Somiibo is another software that does this as well. You can assign a unique session to each tab which means independent proxies, logins, cache, cookies, and everything. This proxy browser is free at the moment.