Do all believers receive the Holy Spirit at conversion but only a few are filled with [empowered by] the Holy Spirit post conversion? Let's trace the Biblical record and then outline the denominational views.
On the 8th day of Tabernacles, Jesus said this to set up our understanding.
In the last day, that great day of the feast, Jesus stood and cried, saying, If any man thirst, let him come unto me, and drink. He that believeth on me, as the scripture hath said, out of his belly shall flow rivers of living water. (But this spake he of the Spirit, which they that believe on him should receive: for the Holy Ghost was not yet given; because that Jesus was not yet glorified.)
Subsequently, at Pentecost, the Spirit was poured out first upon the 12 apostles.
And they were all filled with the Holy Ghost, and began to speak with other tongues, as the Spirit gave them utterance.
Some of the Jews made fun; others wondered about this, asked about it, and received the Spirit also after they believed. Peter replies that the gift of the Spirit is for whoever is called. For them, the pattern was repent, be baptized, receive the gift of the Spirit.
Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost. For the promise is unto you, and to your children, and to all that are afar off, even as many as the Lord our God shall call.
But what about the power of the Spirit (or as the OP puts it “filled with the Spirit”)? After Pentecost, before the conversion of Cornelius, we read this.
And fear came upon every soul: and many wonders and signs were done by the apostles.
This was in keeping specifically with Jesus’ promise to the apostles at His ascension.
But ye [apostles] shall receive power, after that the Holy Ghost is come upon you: and ye shall be witnesses unto me both in Jerusalem, and in all Judaea, and in Samaria, and unto the uttermost part of the earth.
So, at that initial stage, any believer received the gift of the Spirit, but the power of the Spirit was given only to the apostles.
Soon thereafter, Peter and John are arrested, but then released. He tells the others.
And when they [apostles] had prayed, the place was shaken where they were assembled together; and they were all filled with the Holy Ghost, and they spake the word of God with boldness.
The pronoun "they" is a bit tricky to follow, but again, at this stage, it is all who receive the gift of the Spirit, but the power is reserved initially for apostles. But what is happening to the church? The number of believers is growing. The apostles are spread thin. The church is expanding. Squabbles arise.
And in those days, when the number of the disciples was multiplied, there arose a murmuring of the Grecians against the Hebrews, because their widows were neglected in the daily ministration. … Wherefore, brethren, look ye out among you seven men of honest report, full of the Holy Ghost and wisdom, whom we may appoint over this business.
Acts 6:1, 3
They choose Stephen and six others.
And Stephen, full of faith and power, did great wonders and miracles among the people.
We now find that the power of the Spirit has been given to others in addition to the apostles. It is not clear how Stephen received the power of the Spirit.
In another example, Samaria also had believers, but the power of the Spirit had not yet fallen there. Peter and John go there, lay hands, and they are filled with the Spirit.
(For as yet he was fallen upon none of them: only they were baptized in the name of the Lord Jesus.) Then laid they their hands on them, and they received the Holy Ghost.
Simon the sorcerer sees this and asks for the power, but Peter says no that the gift of God is not for sale.
Further, in Acts 9:17 Ananias lays hands on Saul/Paul who receives back his sight. The power of the Spirit continues to operate in believers. Again, it is not clear how Ananias received the power, except otherwise as a gift.
In Acts 10, we read about the start of the gentiles receiving the Spirit and being filled with the Spirit.
While Peter yet spake these words, the Holy Ghost fell on all them which heard the word. And they of the circumcision which believed were astonished, as many as came with Peter, because that on the Gentiles also was poured out the gift of the Holy Ghost. For they heard them speak with tongues, and magnify God. Then answered Peter,
From that conversion, the new believers are baptized in water. This sequence is a change from the earlier Pentecost of repent, be water baptized, receive the Spirit (born-again). It is hear, believe, receive the Spirit (born-again), and be water baptized.
Can any man forbid water, that these should not be baptized, which have received the Holy Ghost as well as we? And he commanded them to be baptized in the name of the Lord. Then prayed they him to tarry certain days.
It is at this point that we have found certain things shifting that might raise other questions such as the relationship of water baptism to the new birth or even the purpose of water baptism, but I will continue to focus on the OP question. To reiterate, “Do all believers receive the Holy Spirit at conversion but only a few are filled with the Holy Spirit post conversion?”
We know so far that the answer is that whosoever believes is reborn; that is, has received the Spirit either at their water baptism or prior to their water baptism. And we know that initially it was only the apostles who were filled with the Spirit as they witnessed to the life, death, burial, and resurrection of Christ Jesus, which is to say, had the power of the Spirit. But as the church grew and expanded across the world, believers would show or prove the power of the Spirit.
Incidentally, this “spread” was foreshadowed in, among other places, Moses appointing helpers (Exodus 18:24-26). It is necessary.
Besides Acts, what do the various epistles have to say about these two actions of the Spirit? These first verses confirm that believers receive the Spirit and are sealed.
In whom ye also trusted, after that ye heard the word of truth, the gospel of your salvation: in whom also after that ye believed, ye were sealed with that holy Spirit of promise,
And grieve not the holy Spirit of God, whereby ye are sealed unto the day of redemption.
Who hath also sealed us, and given the earnest of the Spirit in our hearts.
2 Cor 1:22
The word “earnest” means a pledge, a down payment. The idea is believers are born again, but do not have the full Spirit as Christ did, yet we also know the Spirit gives gifts to believers as separate “events”. We know living waters will flow.
Now concerning spiritual gifts, brethren, I would not have you ignorant.
1 Cor 12:1
The remainder of chapter 12 goes on to describe the gifts, the powers of the Spirit. Paul concludes we should be zealous for the gifts, and then goes on to talk about love.
In short, we found that all believers receive the Spirit, all believers are born-again. This is a tautology, by definition. We also found some are born-again pre or during water baptism.
We also found that initially the power of the Spirit was reserved for the apostles. The reason is they were the eyewitnesses and were commissioned to spread the word and write it down (another subject). Subsequently, as the church grew, as the apostles did as Jesus commanded (start in Jerusalem, Samaria, ends of the world), the gifts of the Spirit manifested in various believers at various times.
Wherefore also we pray always for you, that our God would count you worthy of this calling, and fulfil all the good pleasure of his goodness, and the work of faith with power:
2 Th 1:11
All believers who are born-again have the deposit, all may desire the gifts, and it is God that gives the fulfillment for His reasons.
EDIT TO ADD SO AS TO PROVIDE DENOMINATIONAL INFORMATION OF SCRIPTURES QUOTED:
Evangelical churches or Baptist Churches usually teach a credobaptism, rather than the idea of infant baptism that we might find in Catholic, Orthodox, or other denominations. The contrast is shown in the examples from scripture quoted above where beginning with Cornelius someone who hears the good news and believes the message and is born again by the Spirit and subsequently is water baptized.
There are typically two views on whether the power of the Spirit or gifts of the Spirit have ended. Those who believe in the cessation of gifts believe they terminated when the Bible was completed. It is the idea that only the apostles had the power of the Spirit and once the message was written, the gifts were no longer necessary. Others believe the gifts of the Spirit continue as needed, as the church spread across the world.
Oddly enough, I suppose, cessationism is typically a Protestant doctrine and typically believe in credobaptism, although Pentecostals, like Catholics, would believe the gifts continue, but believe in infant baptism.
So, to answer the OP clearly, all believers receive the Spirit (born-again, have the deposit), but only at times by certain believers are they empowered by the Spirit.