My Mac's Mail app won't add a specific gmail account after upgrading my OS from Sonoma to Sequoia

I recently upgraded my OS from Sonoma to Sequoia. As usual, after a system upgrade, any existing gmail accounts wouldn't authenticate in the Mail app. I would need to re-authenticate those accounts.

I deleted both accounts, and, tried to re-add them. It worked on one account, but, will not work on my other account. I've scoured the internet and have tried several different methods. In every attempt, I get stuck at the final menu, "Choose which apps you want to use with this account." I select which apps to work with this account, but, it never works. It just sits there in that final prompt. It is NOT stuck at that prompt, i.e. if I uncheck a specific app, the blue "Done" button re-lights. But, it will not go thru the authentication process with this particular account.

what is the problem? Anyone know how I can fix this issue? As u can see from the attached screen grab, I've selected which apps I want to use, and, the formerly blue "Done" button is now greyed out. But, nothing happens from there.

Thank you.

[Edited by Moderator]