Be aware: in Chromium browsers, browser extension session storage is leaked into content script processes, and thus can be stolen by websites if they can compromise the content script.
The sky isn't falling, but something to be aware of.
https://bugs.chromium.org/p/chromium/issues/detail?id=1342046 (from https://github.com/w3c/webextensions/issues/72#issuecomment-1762785846)