As far as i know the HD Phantom Menace being shown on tv was put through a digital video noise reduction process by Lucas to look that way. Not a lot to recommend there as it removes fine detail.

Then there are other considerations the way the film shot, the lighting and the grain level of the stock used.

It is entirely possible Lucas used a low grain stock and Lenses that give it that video look.

They did not use the same cameras or lenses or cinematographers on the new movies.

Phantom Menace will continue to look like shit because the digital intermediate used back in 1999 vs the kind of scan Lucas could now do of the original camera negative at 4k a joke. They are claiming a 2k was done back then. Then edited on video by computer. one generation less than the original photography.

The Special Editions master was only 1080P according to Lowry. Lucas never even comissioned a new scan. 1080P to Lucas is good enough for video.