Why can’t Apple TV+ be run like Apple Music? Apple doesn’t hand over millions of dollars for music streaming rights.
Basically, Apple Music is run like traditional radio. Apple TV+ is run like traditional TV/movie distribution. Different businesses (even though they're obviously both part of Entertainment), with different traditions and practices.
The music biz works differently than film/TV. For the most part music lives on royalties/performance rights payments from as many sources as possible - lots of small payments = big bucks. The upfront cost of production is much lower, so the revenue needed to recoup production costs is also much smaller - the record label or artist can fund production without a major investment. Once the music has been released it becomes available simultaneously in physical media, radio, streaming services, juke boxes... effectively everywhere it can be played.
Film and TV have a culture of "initial exclusive rights" - distributors (the major studios, TV/cable networks, streaming services, etc.) underwrite the production costs in return for (limited) exclusive exhibition rights in order to draw an audience solely to their particular platform. In many cases, the producers are pitching their shows hat-in-hand until they find a taker, but for some productions, with big names in the credits or warm receptions at Sundance and other festivals, there may be bidding wars to have the rights to exclusive/first exhibition.
However, if you add up the money that Apple pays in royalties/streaming rights for music... oh, it's a whole lot more than the $25 million they paid for CODA. It's just (usually) pay-as-you-go based on actual listening rather than paying in advance as a bet on the size of the audience that will be attracted. However, when Apple Music does present the occasional exclusive (album debuts, the occasional concert/festival), you can bet they're paying something (either cash, promotional value, or a guaranteed minimum payment) for the privilege.
I guess Apple TV+ can take "credit" for CODA, since they paid $25,000,000 for the rights at Sundance 2021.
It's not as though they developed and produced CODA -- they merely picked up the bragging and streaming rights.
Yes, that's how it works in TV and films. For everything you see. Apple didn't invent this, it's been going on for over a century. Even longer, when you include live entertainment (there's a great satire of this in 'Shakespeare in Love' on the printed playbill for Romeo and Juliet, although it's probably an anachronism). The network or distributing studio or theater gets to put their name at the top of the credits, and the names of a panoply of other producers/studios/production companies follow in succession, based on their financial/deal-making power.
That's true whether the network/studio developed the thing from the ground up, or they picked up a show from another major studio (all the TV network programming produced by Sony, for example), or in a deal with an independent producer (like CODA's).