Cleanly handle context invalidation (extension updates/reloads)

[fregante]

This is mostly a DX issue, but it might appear if the extension reloads while the user has open tabs.

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If I reload the background page, the dev tools and content scripts permanently (?) lose the connection to the background page and should probably be reloaded if possible. The error could definitely be shown more prominently (e.g. a non-dismissible red bar saying "Extension needs to reload")

Now all I get is this when trying to connect to GAPI:

But everything else just silently fails: