The leading "shepherds" (Ezekiel 34) are those who eat the fat of the sheep, and do not feed the sheep, nor heal the sheep, nor keep them from being scattered.
And I will set up one shepherd over them, and he shall feed them, [even] my servant David; he shall feed them, and he shall be their shepherd.
Ezekiel 34:23
Psalm 109 (a Psalm of David)
condemns Paul, not Peter.
Peter, who was made "steward, in charge of the royal household" (Isaiah 22:15 & Mt 16:18), has an heir per Isaiah 22:15-25
Again, David is mentioned:
And the key of the house of David will I lay upon his shoulder; so he shall open, and none shall shut; and he shall shut, and none shall open.
Isaiah 22:22
When the nail is removed the the legacy ends:
And they shall hang upon him all the glory of his father's house, the offspring and the issue, all vessels of small quantity, from the vessels of cups, even to all the vessels of flagons.
In that day, saith YHWH of armies, shall the nail that is fastened in the sure place be removed, and be cut down, and fall; and the burden that [was] upon it shall be cut off: for YHWH hath spoken [it].
Isaiah 22:24-25
The vessels relate to Paul, just as the nail relates to the crucifixion.
But the Lord said unto him, Go thy way: for he is a chosen vessel unto me, to bear my name before the Gentiles, and kings, and the children of Israel:
For I will shew him how great things he must suffer for my name's sake.
Acts 9:15-16
Yeshua pointed out Peter being among the "fat shepherds", when he told Peter to feed, care and shepherd my sheep in John 21:15-16. Peter was set up to fulfill Zech 11:16.
According to that reasoning David was also a fat shepherd (Ezekiel 34:23), which is absurd because David is endorsed by Isaiah:
Incline your ear, and come unto me: hear, and your soul shall live; and I will make an everlasting covenant with you, [even] the sure mercies of David.
Behold, I have given him [for] a witness to the people, a leader and commander to the people.
Isaiah 55:3-4