Yes, that is a symptom of “Preinstalled Apps” getting confused. I still am learning on this, but when a “Preinstalled App” is removed, basically a “stub” is kept (you can find the app still under “All Apps > System apps”) but the actual app is gone (and there is nothing in the app menu). This is needed because as the app is part of the system image, if you just simply removed the app it would be restored when a system update is applied. So an empty placeholder identifying itself as the app somewhat prevents this. What I don’t know exactly is if after a new system update is applied if the “first run” then re-removes the app or if it is don’t a bit differently.
So in the case you are facing, it does seem that “Preinstalled Apps” thinks the app is removed (preventing its display, preventing it from being “installed”) even though it isn’t. That is why I suggested to “yet again” using Preinstalled Apps to “remove / install” with a reboot each time.
I did work with others that got in this situation some time back and could re-create their issue but we couldn’t “get out of it” without a “Factory Reset”. Since then I was sure the devs had implemented some fixes as they did finally re-create the issue. But you are showing there may still be a lingering bug here.
As a “last resort” you may need to use Seedvault to backup data, reset, then restore. Not a very good solution, I know!