Already have paramont plus account, how do I log in?

If you subscribed directly with Paramount through its stand alone app, website or on a non-Apple device, that subscription cannot be directly used with the Apple TV app's Paramount Channel.

The Apple TV app Paramount+ channel requires its own subscription.

Download the standalone Paramount} app to the device and log in with your account there.

Are you trying to log in to stand alone Paramount Apps on your phones or are you trying to log in to the channel in the Apple TV app?

Those are 2 different things, and require different subscriptions.

Where exactly are you trying to log in?

I installed the Paramount+ app on my physical Apple TV 4K and initiated a subscription through their application. Once done, I can watch Paramount+ programming on either this physical device, or streaming via Firefox or Safari on Ventura 13.5 by signing in to their website with the identical credentials used on the Apple TV 4K.

Paramount and Paramount+ are two separate entities and a Paramount+ subscription does not get you into the Paramount channel.

Have you installed the paramount plus app on the Apple TV? Or, on your device?