No Trace Containers by Zakir Khan

No Trace Containers lets you mark specific Firefox Multi-Account Containers as "no history" — pages opened in those containers are deleted from your browsing history automatically, so they never show up in awesomebar suggestions, the History panel, or sync.
Optional per-container settings:
• Wipe cookies on tab close — kill the session the moment you close the tab.
• Wipe site data on tab close — flush localStorage and cache for that origin.
Useful for: research tabs, throwaway logins, work vs. personal separation, anything you don't want polluting your history or autocomplete.

Permissions are used strictly locally:
• history — to delete entries created in marked containers.
• cookies / tabs / webNavigation — to detect container tabs and clear their data on close.
• <all_urls> — required to act on any site opened in a marked container.

The extension makes zero network requests. Source code: https://github.com/ziki17/no-trace-containers