"Home Connect" integration wonky - can't delete integration

I have been using the Home Connect integration, but had some issues. I also had the HACS integration installed (from before it became part of core), so I decided to remove everything, and start fresh. The HACS integration is removed, no problems, but the core integration can’t be removed.

If I try, it shows the “Are you sure?” pop up, but if I click “OK”, nothing happens. It is not deleted. I have tried restarting Home Assistant (before and after trying to delete), but that makes no difference.

I should also note that there is no icon for this integration (while every other integration has the icon present, see below)

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How do I remove this, apparently broken, integration so I can start over? I can find it in core.config_entries, but would removing it from here work? Or would it just be left even more broken, unable to completely remove?