I think there are a lot of levels of complexity here because so many different banks aee involved.
So even if you open an account direct with Charter, you won’t get same day access because Charter isn’t connected to BACS (I think I’m right in saying that). The way you can tell is if you open an account with Charter, you don’t get a sort code and account number - instead you get Charter’s generic sort code and account number, plus a personalised “reference number” which refers to your Charter account.
So when you make a withdrawal from Charter, it doesn’t come out straight away. Instead, Charter send the money via their bankers - for example Barclays and that gets processed in a batch once or twice a day.
So what happens when you move money out of a pot is: Monzo communicate with Charter, Charter send the money via Barclays in a daily batch. The money reaches Monzo ans lands in your current account.
I think I’ve got that right.