I'm experiencing the same thing with my Pixel 9a. I've been able to use the Dasher app until yesterday when this login loop issue appeared.
I've cleared the cache and data, reinstalled, reset my phone, and turned on exploit protection compatibility mode, but nothing seems to work.
I remember experiencing something just like this on my Samsung a few years ago, so I'm willing to bet it's a problem on Doordash's end, but who knows.