Hello!
For clarification, are the two windows in your video are separate user accounts? One that you ran the !conda install inside and one that you didn't? Notebook environments are culled after a period of inactivity and rebooted when a notebook is opened, so there is generally no need to manually reinitialize. Are you finding that your broken notebook is persisting after being inactive for a while?
Could I get some more info on how you installed psycopg? did you specify a repo? I haven't been able to install psycopg with just !conda install psycopg due to missing packages, but I was able to install psycopg2 and haven't experienced any kernel issues alongside it. Is that an option for you?