Can't sign my Apple ID in on Safari (Mac OS 14.3.1)

I'm a long time Mac user and have a long-established Apple ID that I use as the login for a number of online services.

Today I signed up for a service (TIDAL Music) via my Windows PC's desktop browser, and I created my account as a "Sign in using Apple". I'm able to sign into my Apple ID just fine on this PC, and on my iPhone.

I went to sign into my TIDAL account on my Mac (since that's connected to the good speakers!) and when it asks for my password, I enter my password and then get the dialogue box shake that indicates an error, but without any alternatives presented.

I know I'm entering the correct password; I have double checked I'm not using capslock or mis-typing, and I even resorted to copying and pasting directly from my secure password manager. Still no success.

I am still running Sonoma 14.3.1 and I have seen google search results that suggest the problem might be that the dialogue box isn't giving me the option to use/add a 2FA verification code. (My account does have 2FA turned on.) I am not sure how to get around this, and I'm not even sure if that is the problem.

I'd rather not have to update my MacOS if I don't have to, as it's an ageing machine and I have everything set up the way I like it. Are there any other solutions to my problem?