Although JD Payne, Patrick McKay, and the rest of the TRoP crew were legally prohibited by the Tolkien Estate from directly working with Peter Jackson himself in any capacity (something they had tried to do on a Consultory basis before being told to cut off all contact), there was no way for the Tolkien Estate to legally regulate the production's choice of filming locales, effects and prop houses to partner with, etc , which allowed Payne and McKay and their team to work with WETA Workshop and John Howe (who had continued to do freelance design work for WETA) and Howard Shore (who conposed and performed the series' Opening Titles theme), thus allowing them (Payne and McKay) to create a Spiritual connection between The Rings of Power and the Jackson films through the series' design and production in lieu of an Officially sanctioned one. They were also able to choose to film the first season in New Zealand, further establishing a Spiritual link between the series and the Jackson films.
Establishing Shots of New Zealand locations also continue to be used even after the production's move to England for Season 2+ and WETA continues to remain involved tangentially through the production's new UK-based prop houses maintaining the aesthetic that WETA and Howe established.
TLDR, it's very much intended for TRoP to exist alongside the Jackson films even though no formal official direct links between them can be legally established, which is why I referred to TRoP as being a Spiritual Companion Piece to the Jackson films.