You are attributing the type/shadow of Eliakim to Peter instead of Christ?
Isaiah 22:
20 ‘Then it shall be in that day, That I will call My servant Eliakim the son of Hilkiah; 21 I will clothe him with your robe And strengthen him with your belt; I will commit your responsibility into his hand. He shall be a father to the inhabitants of Jerusalem And to the house of Judah. 22 The key of the house of David I will lay on his shoulder; So he shall open, and no one shall shut; And he shall shut, and no one shall open. 23 I will fasten him as a peg in a secure place, And he will become a glorious throne to his father’s house.
The only glorious throne to his father's house is the One Christ sits on. Jesus Christ promised Peter one of the 12 thrones to judge Israel. Not "THE" throne. Plus the throne discussed is specifically in Jerusalem and over the house of Judah. There is only One who can take that throne...Messiah Jesus Son of the Living God born of the House of Judah.
But I understand what you posted is a personal interpretation of an OT text applying an eisegesis Unless you have an infallible interpretation of the RC magesterium you would like to provide?
Catholics use the entire bible as a cross reference to understand the context of a verse; they do not just pick verses out.
If so then you would not object to a bit of exegesis.
Isaiah 22:
22 The key of the house of David I will lay on his shoulder; So he shall open, and no one shall shut; And he shall shut, and no one shall open.
Revelation 3:
7 “And to the angel of the church in Philadelphia write,
‘These things says He who is holy, He who is true, “He who has the key of David, He who opens and no one shuts, and shuts and no one opens”: 8 “I know your works. See, I have set before you an open door, and no one can shut it; for you have a little strength, have kept My word, and have not denied My name.
Is the above from Revelation chapter 3 also Peter and/or successors?
Which is another parroted papal polemic by RC posters, but which is not even an officially binding interpretation as far as I know.
There is no special sense in which binding and loosing is ascribed uniquely or newly to Peter, except what RCs read into the text, nor apart from the magisterial judicial aspect which flows from the OT, (Dt. 17:8-13) was the spiritual power of binding and loosing restricted to the magisterium, as it is provided for all righteous disciples. (Mt. 18:19,20; Ja. 5:16-18)
The city to which Peter was given the keys was the heavenly city itself. This symbolism for authority is used elsewhere in the Bible (Is. 22:22, Rev. 1:18).
Which key is the gospel, by which one is translated into the kingdom of Christ, (Col. 1:13) and which all are called to preach.
As for Is. 22,
while the language and concept of a key and policing authority seen in Is. 22 is used in Mt. 16:18,19 this does not make it a prophecy of Peter's power (Paul even used language of the Philistines), much less necessitate that the real subject will have successors.
For instead, not only was this prophecy of Eliakim's ascendancy apparently fulfilled in the OT [as 2Ki. 19:1 2Ki. 18:18, 2Ki. 18:37 and Is. 3622, 37:2 all refer to Eliakim being over the house, (bayith, same in Is. 22:15,22) which Shebna the treasurer was, (Is. 22:15) and evidently had much prestige and power, though the details of his actual fall are not mentioned [and who may not be the same as "Shebna the scribe" (sâkan) mentioned later] - but the text actually foretells:
"In that day, saith the LORD of hosts, 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 the LORD hath spoken it." (Isa 22:25)
Whether this refers to Shebna or Eliakim is irrelevant, for in any case it means that being a nail that is fastened in the sure place does not necessarily denote permanency, as it did not here.
Yet if we are looking for a future fulfillment with permanency, both the language concept of a key and being a father to the house of David corresponds more fully to Christ, and who alone is promised a continued reign (though when He has put all His enemies under His feet, He will deliver the kingdom to His Father: 1Cor. 15:24-28).
For it is Christ who alone is said to be clothed "with a garment down to the foot, and girt about the paps with a golden girdle," (Rv. 1:13; cf. Is. 22:21) and who came to be an everlasting father to the inhabitants of Jerusalem. (Is. 22:21; cf. Heb. 7:14; 8:8; 9:6) And who specifically is said to be given "the key of the house of David," "so he shall open, and none shall shut; and he shall shut, and none shall open," (Is. 22:22) as He now “hath the key of David, he that openeth, and no man shutteth; and shutteth, and no man openeth.” (Rev. 3:7) and is a nail in a sure place who sits in a glorious throne in His father's house, (Is. 22:23; cf. Rv. 3:7) And upon Him shall hang “all the glory of his father’s house, the offspring and the issue, ” (Is. 22:24) for He is the head of the body, the church, (Colossians 1:18) "from whom the whole body fitly joined together and compacted by that which every joint supplieth,“ (Eph. 4:16) and in Jesus Christ dwells "all the fullness of the Godhead bodily.” (Col. 2:9)
Thus neither Eliakim nor Peter are shown having this manner of fulfillment, nor does it necessarily denote successors (Christ has none Himself, but took over from the Father). Thus if this " a nail in a sure place" corresponds to anyone future then it is Christ, and nothing is said of Eliakim having a vice regent. Thus this prophecy is actually contrary to Peter being that Eliakim.