Same problem here on my 2019 MacBook Pro 15''... I have had this problem for over a year now, and I still have it plus more. Not only do I still have to do the "reCAPTCHA-20 TIMES A DAY", but google search and my Gmail account, for the matter, won't acknowledge or recognize that I own all Apple products, not Android/Google products.
My biggest problem with all this mess is even before returning to a Gmail/Google account again I tried using just an "@iCloud Email Only" as my email and applied it while using my Mac and iPhone only as my devices..... So ALL APPLE 100%, and yet, among a ton of other issues I was still getting "reCAPTCHA"...... All while troubleshooting with Apple Support for over a year. Again remember I had no Gmail account, no Yahoo account and, no Outlook account, and I still can't go 15min without getting caught up with tons of Errors, reCAPTCHA's, Kernal Panics, Beachballed to death, hanging apps, freezing system, passwords changing on there own, putting a third party email as a "REACHED AT ONLY" on my apple account, then next time one of my devices ask for a password, for one reason or another It whips my (reached-at email) up to the top of both my devices as my appleid and takes my @icloud, which was my true appleid user sign-in and makes it an alias. I'am Apple **** and I can't find the freaking front door.