The docs are very unclear about this. I get that you can autoupdate your extension by bumping the version number if you self host your extension. However what I don\'t know is i
When you publish to Chrome Web Store (CWS), CWS hosts your extension and you loose control over update_url attribute in manifest.json
(it's overriten by CWS specific link). When you decide to make new version of your CWS-hosted extension available, you simply upload it (with higher version number) to CWS (via developer dashboard). After that, you just wait for Chrome auto-update feature to do all the work.
Each Chrome performs, in the background and without users direct permission, a routine checks in CWS (or somewhere else if extension is self-hosted) making sure that all extensions are up to date. If new version of any extension (or app) is available, Chrome performs an auto-update (if extension's permissions haven't increased).