strangely if you search star trek prodigy on paramount plus (in my case as an addon to my primevideo subscription) - episodes s1e03 and 04 are available and play fine. The rest are marked unavailable as expected.
I’m guessing its a mistake, but would be cool if this were an indication of something happening
Prodigy has been removed from Paramount Plus.
Technically yes they do own Star Trek, but the way the accounting works is they sell the broadcast/streaming rights back to themselves. It’s a bit convoluted, but taking the rights away from their own service means CBS as a studio can either resell it to another broadcaster/streamer or failing that write it off for tax purposes.
It sucks, but all the studios rig it up this way