I like to casually read through updates in my inbox, when it's convenient for me, so I would like an option to get all email notifications, filtered into their own label. But I also want any notifications from e.g. tasks that directly involve me as a subscriber to not be filtered.

While a custom header would be perfect for this, gmail unfortunately doesn't have filters on custom headers. GitHub has a workflow for its notifications where any notifications I'm directly subscribed to are To: me, and anything that I've simply opted into is Cc: me. That way, my filter can be: "from:phabricator -to:me".