Savings, actually. My bank allows you to have as many savings accounts as you want and you can open 'em all online. So I have like 7 savings accounts tied to my current checking, that all have the bill $ auto-deposited. About half are auto-debited as well. I'm about to transition my active checking account - I noticed with all the linked savings it's really easy to shuffle the money and play "funny money" if I'm short - so I'm severing that link and just opened a new fee-free checking at another bank. Once I fund it with DD and get the card, I'm going to cut up/hide my old debit card to make the bill funds more difficult to access.
Credit score absolutely no, IRS probably not, honestly totally happy to finance nerd out with you in PMs/DMs/text. If they were all checkings there would be more potential for credit score impact but honestly that would depend more on the account and tied functionality (like if there was a tied line of credit to the account(s).) there is also a separate system banks use to rate depositors (much like a credit score but for - well, deposits instead) however maintaining multiple accounts shouldn’t impact that negatively.