WI: Henry VIII has a daughter from Catherine Parr

Parr being Henry's last wife, and the one to which he died married, what if she had borne him a daughter? Despite the Elizabeth-Mary-Anne obsession of the period, let us call her Eleanor.

She will presumably be raised Protestant, and be fully legitimate, as Henry had no severe grievances with his last wife.
How does this change the dynamic of the Tudor siblings? Does she fully supplant Elizabeth?
I believe Elizabeth would have had no base of her own, if not for her status as the Protestant in opposition to Mary.

Does she succeed Edward if he dies on schedule, or is there struggle, presumably initiated by Mary?
She has a superior position to Jane Grey, but I do not know if that would save her if Mary rebels anyway.

She would be ahead of Mary in the succession. Mary would also have difficulty rebelling since she’d be going against her father’s will, but the age of this daughter lends itself to a chaotic regency, especially if Catherine Parr still marries Thomas Seymour.

I mean, very unlikely. Henry was very old and sick, and everyone felt that it would be impossible for him to even try to conceive a child. I'm not even sure he consummated the marriage with Parr. She was much more of a nursemaid than a wife.

But yes, she would be ahead of both Mary and Elizabeth, and Edward's regents would try and find a husband as soon as possible. Thomas Seymour is not a man I want near the regency, so I doubt Catherine would be able to marry him - or, at the very least, not for several years.