What sort of browser extension would that be?
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Tampermonkey? Just enter that word in your extension repository. If you can run my homebrew extension, I am assuming you use Chrome. So that would be https://chromewebstore.google.com/search/Tampermonkey
It lets you use user scripts that do some stuff an extension would do and provides some mechanisms to use capabilities only extensions can use. Like storage. The advantage is, that the same script will run on Firefox and Chrome and others. It should also work in other user script addons, like Greasemonkey.
It is rather popular, on Chrome it has over 10 million users.