Kingdom of Priests

You have made them into a kingdom and priests to our God, and they will reign upon the earth. Rev 5:10

He (Jesus) made us into a kingdom, priests to his God and Father Rev 1:6

These are the end of days when Jesus is coming to begin the Kingdom in earnest - Satan is banished for 1000 years (Rev 20:7) and his kingdom, (he was the god of this world) will be finished.

The kingdom has not yet begun and therefore the priests are not yet "reigning" either.

However, this does not change what God has begun in His 'called out' people. Those who are in Christ and live faithfully till the end, are already living roles of intercessors between God and men. You refer to 1Pet 2:9; we see in 1Pet 1:3 who this is directed to and that this is yet future - 'reserved in heaven'...

He has given us new birth into a living hope through the resurrection of Jesus Christ from the dead, 4and into an inheritance that is imperishable, undefiled, and unfading, reserved in heaven for you 1Pet 1:3

These are called to live out in preparation the ways of God for the responsibility to be entrusted to them when they reign with Jesus at his return. A priest is to live faithfully the ways of God and to avoid being swept up in the world of sin. This is the life expected of those who are God's - given to Christ to form the body, the church built on the foundations of the prophets etc Eph 2:20

the whole building, being fitted together, is growing into a holy temple in the Lord, 22in whom you also are being built together into a dwelling of God in the Spirit. v21

Where do the priests serve? In the temple - the spiritual temple which is Jesus and his saints.

OP: But are we a royal priesthood today? (1 Pet 2)

Yes.

OP: Is Paul saying we are priests today through Jesus or, to put it another way, spiritually, are we a Kingdom of priests

Yes.

As the OP mentions, God desires and seeks a kingdom of priests who worship in spirit and in truth (John 4:23-24).

Fast forward to the Israelites redeemed from Egypt at the Passover. Some 40 days later they arrived at Mt. Sinai to receive the Law. God would offer a conditional covenant, and IF-THEN covenant.

Now therefore, if ye will obey my voice indeed, and keep my covenant, then ye shall be a peculiar treasure unto me above all people: for all the earth is mine: And ye shall be unto me a kingdom of priests, and an holy nation. These are the words which thou shalt speak unto the children of Israel. Exo 19:5-6

The people agreed.

And all the people answered together, and said, All that the LORD hath spoken we will do. And Moses returned the words of the people unto the LORD. Exo 19:8

But they became scared at the LORD.

And all the people saw the thunderings, and the lightnings, and the noise of the trumpet, and the mountain smoking: and when the people saw it, they removed, and stood afar off. And they said unto Moses, Speak thou with us, and we will hear: but let not God speak with us, lest we die. Exo 20:18-19

So, they asked for an intermediary. The Levitical tribe was assigned the priestly job. The other tribes became the children of Israel; they were not priests.

And take thou unto thee Aaron thy brother, and his sons with him, from among the children of Israel, that he may minister unto me in the priest's office, even Aaron, Nadab and Abihu, Eleazar and Ithamar, Aaron's sons. Exo 28:1

So, the plan of God to have a kingdom of priests didn't initially happen. It took Christ Jesus of the line of Melchizedek, not Levi, to fulfill the Law, to make possible for believers to become priests also of the Most High God. The Book of Hebrews draws many distinctions between the two priesthoods.

And Melchizedek king of Salem brought forth bread and wine: and he was the priest of the most high God. Gen 14:8

So, to answer the OP, Paul realized that the Law could not make him righteous, nor could it make him a priest. But in Christ, this was possible.

And be found in him, not having mine own righteousness, which is of the law, but that which is through the faith of Christ, the righteousness which is of God by faith: Phil 3:9

Ye also, as lively stones, are built up a spiritual house, an holy priesthood, to offer up spiritual sacrifices, acceptable to God by Jesus Christ. 1 Peter 2:5

And hath made us kings and priests unto God and his Father; to him be glory and dominion for ever and ever. Amen. Rev 1:6 And the LORD commanded us to do all these statutes, to fear the LORD our God, for our good always, that he might preserve us alive, as it is at this day. And it shall be our righteousness, if we observe to do all these commandments before the LORD our God, as he hath commanded us. Deut 6:24-25

As far back as the Exodus out of Egypt, God describes Israel as a kingdom of priests and a holy nation (Exodus 19:6). Later, Peter addresses Jewish believers in Christ: “But you are a chosen people, a royal priesthood, a holy nation, a people belonging to God, that you may declare the praises of him who called you out of darkness into his wonderful light” (1 Peter 2:9).

Peter then goes on to explain that this kingdom of priests, this holy nation, is not restricted to Jewish believers in Christ. Paul was commissioned to take the good news of the kingdom to Gentiles scattered around the Roman Empire. John wrote to the first century churches explaining that they – Christians both Jews and Gentiles – are included in this kingdom of priests:

To him who loves us and has freed us from our sins by his blood, and made us to be a kingdom and priests to serve his God and Father, to him be glory and power forever and ever! (Revelation 1:5-6)

In Revelation 5:9–10 it says God has redeemed people from every tribe and tongue and people and nation, and they are included in this kingdom of priests.

There are some Christian denominations who believe that God has finished with Israel and this kingdom of priests, this holy nation, is now “the Church”. Whether that embraces all Protestant churches, all Roman Catholic churches, and all Eastern Orthodox churches, I could not say. Just because a person self-identifies as a Christian does not mean they are automatically part of God’s kingdom of priests.

In order to see the Kingdom of God, a believer has to experience the new birth. This is a spiritual rebirth, an act of God whereby eternal life is imparted to the person who believes (2 Corinthians 5:17; Titus 3:5; 1 Peter 1:3; 1 John 2:29; 3:9; 4:7; 5:1-4, 18). John 1:12-13 indicates that being "born again" also carries the idea of "becoming children of God" through faith in the name of Jesus Christ. When a Christian is born again and spiritually renewed, they become a child of God by right of the new birth:

Therefore, if anyone is in Christ, he is a new creation: the old has gone, the new has come! (2 Corinthians 5:17).

The “selection process” is rigorous. Much is required of those who have been adopted into God’s family and who seek to serve Him, both now in this world, and later, in the world to come. As we declare the good news of God’s kingdom and point others to Christ Jesus, we belong to this kingdom of priests now, eagerly awaiting that time when we will appear with Christin glory.

If then you have been raised with Christ, seek the things that are above, where Christ is, seated at the right hand of God. Set your minds on things that are above, not on things that are on earth. For you have died, and your life is hidden with Christ in God. When Christ who is your life appears, then you also will appear with him in glory. (Colossians 3:1-4).

From the above I can only conclude that God intends for all who serve Him now, as ambassadors of the kingdom of God, to fulfil a priestly role here on earth by declaring the praises of Him who has called us out of darkness into His wonderful light.

In answer to your question, yes, through our active faith in Christ Jesus, we are part of this spiritual kingdom of priests. The glorious reality of this Kingdom of Priests, this Royal Priesthood, will become manifest when we go to be with the Lord.

Edit to clarify "The selection process is rigorous": I do not intend to suggest we have to work at our salvation in order to earn it. Salvation is not a process. It happens in a moment, entirely due to God's initiative. Rather than just delete that sentence I thought to explain myself better.