Is it possible to save cookies, local storage, cache, etc? For all sites or better for only a particular site? Using the Tor browser with the Whonix Workstation?
Maybe possible to load cookies and state from a file saved somewhere?
I tried setting Network.cookie.lifetimePolicy to 0, but it gets reset by itself.
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Not really becuase it goes against how the TBB was designed. Ask upstream if there is a way to sabotage the privacy protections 
Preferences > uncheck “Always use private browsing mode”.
You can then set per-site cookie persistance the Firefox way.