Nope.
If something should happen to William after he is crowned and George is not of age very likely Kate would be his Regent.
The holder of the title of Regent does not have to be a relative or royal or even one person. It as been held by a Committee before.
That is not what I keep reading
Regency Act 1937:
3 The Regent.
(1) If a Regency becomes necessary under this Act, the Regent shall be that person who, excluding any persons disqualified under this section, is next in the line of succession to the Crown.
and for example
and more
https://royalcentral.co.uk/uk/will-harry-and-meghans-decision-lead-to-a-new-regency-act-135996/
I believe you are correct. William’s children come before Harry so Kate would be Regent until Prince George, who is currently 3rd in line, came of age. Harry is currently sixth in line, barring Kate having further issue. Harry will never see the crown.