I’m curious why you need two accounts to switch from public to private relays. Nos and I believe Amethyst allow you to post to specific relays. Nos also allows you to read from specific relays. Damus has some of this functionality as well.
Discussion
So I can switch relays with one click by switching accounts (every account has different set of relays).
So it would be possible to distinguish what relays you are using by looking what account is active currently.
To not accidentally post something stupid or private to public relays.
Would better UI help to distinguish between where you are posting?