DirecTV still has a suite of linear Showtime multiplex channels: Shoetime 2, Showtime Extreme, Showtime Family, etc. I haven’t seen any indication of branding changes for those channels, if any.
I have the full Paramount+ with Showtime package (via a Black Friday deal through Verizon). The live streaming only includes the East and West feed of the main Showtime channel.
The Paramount+ app on Apple TV works fine for me. My only issue is that the promos that play at the beginning of shows/movies are not skippable - other streaming services don’t have those (on their ad-free tier) or allow skipping them.