To be honest, I’m not interested in whether they’re separate accounts or not, the UX isn’t great at the moment though, and that should be really simple to fix.
If paying a bill from a pot, I want to see that as a payment from the pot.
If that means that behind the scenes you need to mask a withdrawal to the main account as a payment, so be it.
If that’s not allowed, at least a tag to say which bill it’s intended for.
Also, within the pot, it’d be nice to mark paid and unpaid bills for at a glance planning