How to watch paramount plus through AppleTv Channel on Laptop running ATV app?

I bought the Paramount+ subscription through apple.

That statement is more ambiguous than one might think. If you subscribed in the Paramount+ app on an Apple device, then your subscription is valid for the Paramount+ app on Apple devices. It is not valid for the in-app Channels of the same name inside the Apple TV app. Those are only valid with a subscription started in the Apple TV app channel. These are different types of subscriptions with different terms and conditions, different perks and limitations, and are not exchangeable as such.

It may get a bit confusing on iPhone, iPad, Apple TV box, where external “connected” apps and in-app channels are mixed in one interface (“Explore Channels & Apps”), with very little to set them apart. Even more so when the same content provider name is used for both a channel and an app.

There is no place to login, the only choice is to subscribe, and I'm concerned it'll double bill me.

The various types of subscriptions to one service can exist simultaneously, and you could be double-billed.

If you had subscribed to the in-app channels of the Apple TV app, then that would be active by being signed in to the Apple TV app with your Apple ID (on Mac: menu Account). Channels have no other sign-in.

You’ll have to make a choice: Subscribe to the Apple TV app Channel (and use the Apple TV app), or subscribe to the Paramount+ app (and use their app), or subscribe with Paramount+ directly (and use their app).

As there is no Paramount+ app on Mac, you would then be using the browser for some types of subscriptions.

It works on mine. I just tested to make sure there’s no issue. Since you’re subscribed through Apple TV I would try signing out and signing back in. In the left pane in the Apple tv App at the very bottom you should see your user account. Or just sign in through that pop up box. Or use the Account at the top of your screen to sign out & sign back in. You should see your Paramount Channel in the left pane under the Channel tab - click on that to reveal your Channels. You’re not scrolling around looking for icons

If it’s still not working Quit the App and restart MBP