There is a simpler answer which is that this stuff is overblown PR.
Rangnick said, of Jurgen Klopp, "
I was not his mentor – that was a coach called Wolfgang Frank – but we have always been in contact and had a good relationship with each other."
Of Tuchel, Rangnick said: "He was one of my players at Ulm,
unfortunately only for six months." Rangnick then hired him as youth coach at Stuttgart. Tuchel joined in 2000 and Rangnick was fired in early 2001, so their paths did not cross very long. Since then Tuchel has had his own career elsewhere and has never worked under Rangnick afaik. He's not a mentor, he's a guy who gave him a job.
Then you have Nagelsmann, whose coaching career began when he joined Hoffenheim in 2010 (right around the time Rangnick was leaving that club) and then moved to Leipzig many years later. He actually worked with
Tuchel at the beginning of his career, and you can find references to Tuchel being
his mentor (even though Nagelsmann has explicitly said Tuchel was
not his mentor).
Judge managers by what they actually do, not by who the press said they influenced or were "mentored" by.