Sorry to hear that you’ve been having issues with your H9000.
If you go to page 65 of the H9k manual, you will see a section titled “Using the H9000 with your existing audio interface.” This should clear up the issue you're having with the "USB audio is muted” error. The most important part of setting this up is the last step, you must make sure that the new aggregate device you’ve created is set to the correct sample rate or you will get the "USB audio mute error.” Sometimes you will need to nudge sample rate back and forth for it to be properly synced. You shouldn’t have to turn on the H9k before your computer or audio interface for this to work correctly.
Have you tried connecting your H9k via Wifi and if so is Emote still disconnecting then?
Do you have any other external hardware that you can try using with the Logic I/O you’ve described? If you try sending audio to a different external effect and you're still having issues then that will help determine if the issue is with the H9k or your DAW settings. It doesn’t look like your using the I/O plugin in Logic which could be the issue, here’s a tutorial I found that could help – https://www.youtube.com/watch?v=eL1joHN-7z4&ab_channel=MusicTechHelpGuy
I looked at the audio interface you're using and I would also recommend connecting the World Clock terminals of your audio interface and H9k so they will automatically be synced, this will make things easier when you are changing sample rates. You could also try connecting your audio interface to the H9k via ADAT for a simple means of having 8 channels of I/O. This has been my preferred way of using the H9k recently.
From your screenshots it looks like your using BigSur. We don’t officially support BigSur for Eventide software yet but we are currently testing for bugs.
The H9k can be a bit tricky at first but combined with your audio interface you will have a very powerful and versatile studio setup once you’ve figured everything out. Hang in there and you will have a wonderful machine to work with!
I hope this response is helpful. You can always email firstname.lastname@example.org for direct support as well.