This is great: I've wanted a personal extension for a while (roughly to replace my userscripts but with more power and better sync) but was put off by it having to be public or manually installed. Now I can make this!
I have a few private extensions like this (e.g. for HN, GOG, my own new tab page, etc.). I don't have the exact steps for this at the handy, been meaning to do a write-up at some point, but my mk script is just "$webext sign --channel unlisted --api-key $jwt_issue --api-secret $jwt_secret" – I don't recall if you need to create it the extension in the Mozilla web UI first, but I don't think so(?)
Edit: I successfully signed the key on AMO. Here are the steps:
Get an access token from https://addons.mozilla.org/developers/addon/api/key/
In manifest.json, add browser_specific_settings.gecko.id and set it to something like "myext@example.com"
Run command: web-ext sign --api-key=<jwt-issuer> --api-secret=<jwt-secret> --channel=unlisted
That command will upload your extension to AMO. After an automatic review, you can download the .xpi file from AMO.
Yeah, not entirely sure how this works. I've been doing this for a few years with a bunch of extensions, and thus far it's always just been automatically approved (although that does take a few minutes).
Even prior to this there was an option to upload an extension to AMO for "private distribution". Mozilla will sign your extension so it installs without a fuss, but it won't be hosted on AMO. You can still host it on your personal website, or share the .xpi file though.