I agree there are similarities or maybe we can call it the foreshadowing of things to come since this covenant was in the making from Genesis_3:15.
Not so sure as to the whole triple priesthood in the new covenant. I am not saying there is not ….it is just that there is no mention of high priests in the 7 church epistles (Romans -Thessalonians) Hebrews does give reference as it is addressed to the Jews of the dispersion and Acts only gives reference when speaking about those in a position. The 7 church epistles are completely void of any mention of high priests or priests.
I believe the reason for that is the temple is not a physical structure during this administration of grace. We →the body of Christ are the temple, the holy naos and when the epistles refer to the individual believer it calls us the tabernacle….The temple ceased to be a physical structure after Pentecost and it will revert back to the physical building after this administration ceases, which is when Christ returns in the air for the church of God (rapture) it is then the beginning of sorrows begins.
The Ministerial priesthood you mentioned are gift ministries of apostles, prophets, evangelist, pastor, and teachers these gift ministries are services to Gods people on a horizontal lever…. also in effect until the end of this administration.
The office of bishop is a perfect priest and shares in the high priesthood of Christ over the low priests, also Christ wore the seamless garment of the high priest, the body of Christ is the temple, we are his mystical body, the church is eternal cos it’s founder is eternal, why does scripture picture a temple, altar, ark etc in heaven? There is a distinct separation between the ministerial priesthood and that of the royal priesthood people
Matthew 22:14
For many are called, but few are chosen.
Matt 13:11 He answered and said unto them, Because it is given unto you to know the mysteries of the kingdom of heaven, but to them it is not given.
Jn 20:21 as the father sent me, I send you. And Jn 17:18 I send you!
(The apostles with the same minisrty, power, and authority)
The apostles received the kingdom.
Lk 22:29
The apostles administer the kingdom. Matt 16:18-19 & 18:18
The apostles govern the church.
Matt 28:19-20
The apostles hold office.
Acts 1:15-20
The apostles have authority to forgive sins. Jn 20:23
Apostles are the light of the world!
Matt 5:14
The apostles are Christ’s successors!
They have authority to send others as well, apostle means one who is sent!
Therefore the apostles have authority to send more apostles or successors!
Apostolic succession!
The nations still need to be taught, disciples still need to be baptized and the church the new covenant kingdom of christ still needs to be governed!
Three fold ministry,
Teaching:
Sanctification:
Governing:
Keys of authority! And power to bind and loose! Matt 16:18 and Matt 18:18 matt 28:19 Isa 22:21-22
Moral authority:
(Teaching)
Necessity of being taught by Christ:
Two edge sword: defining truth and condemning errors, and Interpreting scripture.
Jurisdictional authority:
(Governing / administering)
Necessity of Peter and the apostles and their successors to govern the holy church.
Spiritual authority:
(Life of Grace)
Sanctifying thru the mass and Sacraments
God established order and peace and knowledge of truth in a hierarchical authority of Peter and the apostles!
There is a hierarchical authority in all that God has ordained!
hope this helps