Not a great solution to constantly have to top up your checking account with some amount between "I need this much to pay my bills" and "losing this amount would devastating" which for many people has quite some overlap

If most of your income comes from salary/wages, just have the paycheck first hit your normal checking account first and then have scheduled deposits from there into savings accounts someplace else. You generally have enough money in the account to cover your monthly stuff plus a bit of buffer, but have the pile of cash elsewhere in case something happens.

This way you're not actively having to top off your normal spending account, but at the same time have a backstop in case that active account gets hit by fraud or whatever.

I'd suggest protecting yourself even further and having those accounts be split across two different banks. This way if one of your bank credentials gets hacked or you have some issue with the bank you at least have a chance of still having an account with cash someplace else to cover the short term.

You can pay bills from your savings account with ACH in the US.