Shaafdiesel To be frank, there's only so many options:
1) If you have on-prem Exchange servers still (licensed & with DBs, not just the management-only free license), you can simply bring the mailbox back on-prem. (Or use another mail host/mailbox/email address elsewhere that allows basic auth)
2) Stop using the vendor and migrate elsewhere if they do not stray away from a hard basic auth requirement. (Which given how many business customers are in M365/Exchange Online these days, that sounds like a nail in the coffin for losing customers... I can't imagine "no" is going to be many vendors' final answers to this)
I know #2 is easier said than done when customers can only have so much influence and some services just don't have alternatives, but that's what you're looking at.