Nah dude. Argue as much as you may, the only thing we can factually agree on concerning these films is that they are all separate adaptations from any other film or book material. It is not like the Star Wars trilogy, because Star Wars is one single canon and not a multiverse situation where the rights are being shipped off to different companies. Marvel is a multiverse, and both in-universe because they literally designed a Multiverse, and outside of it in terms of multiple companies having different rights for different characters and properties. Star Wars is one single canon, with anything existing prior in the Extended Universe being considered non-canon branded as 'Legends'. And yes, it's a very sore point for OT fans that Greedo Shot First is the canon because George Lucas decided to retcon it, and it has not been officially reverted since then.
Rings of Power is making use of its own story through its own specific liscencing deal, and does not officially connect with any other existing property. PJ's LOTR is not canonical to the books or to Rings of Power either. Only PJ's Hobbit trilogy is canonical to his LOTR trilogy. And let's be clear that PJ's LOTR isn't the only adaptation that's made it to film; there did also exist the Rankin Bass Hobbit and the Ralph Bakshi LOTR films as well, which I will use as examples of other adaptations that aren't connected to anything else. All of these films are separate adaptations.
If the Amazon Rings of Power wants to write itself in a way that tries to work with the Peter Jackson films, then all power to it. But it's clear that they are not actually connected in any way other than grandfathering designs from the films, and sourcing the same book material to build its story around. It doesn't default in being connected to the PJ movies just because they share some design elements and some of the artists who created it, and brought back Howard Shore to do the music for the intro. That isn't what connects these properties together.Once Amazon announces a plan to remake LotR themselves into a show, I'll agree. For now though, the visuals make for a connection that cannot be ignored. You say you figure it was part of the licensing deal, but is there proof that Amazon fought against having their show in any way tied to the Peter Jackson movies? They certainly would have been the ones who made the decision to bring on people like John Howe.
When it comes to the divergences, we come back to my giving them the opportunity to make things line up IN THE END. I understand that you're saying we shouldn't assume that the show will conclude in such a way that seamlessly ties to the movies, but at the same time we can't yet say that will not happen. My HOPE is that they will aim for a connected story, and evidence so far doesn't sway from that. But I guess we'll see over the next several years.
Amazon does not have Jackson's involvement directly, and Peter Jackson himself was part of the writing force behind the movies. Amazon is not molding their story to fit with the Peter Jackson trilogy either, as they have not outright stated any intent to even do so and the show so far hasn't done anything to bridge a connection outside of use of designs or literally picking out bits of dialog as a straight out callback to the movies. There isn't actually any plot that connects specifically to the movies.
Design connections don't make them connected. Liscencing deals can offer the shared use of existing designs without having all properties be canonical to each other.
One example is the Games Workshop Lord of the Rings Tabletop game, which made minis directly based on the PJ LOTR movies, but it also expanded itself to create figures and lore the PJ movies did not cover, like designs for new creatures or elaborating on the individual Nazgul, like a unique design for Khamul the Easterling who was never given any distinct form in the PJ movies
The Tabletop borrows heavily from the Peter Jackson films, but is not canonical to them. It also builds its own canon.