The Q asked is a simple one that requires little biblical effort to answer. However, the answer will oppose long-held beliefs which run contrary to the testimony of Scripture.
There is no clear, unambiguous case for a divine 'person' the Holy Spirit who is separate from the Father. There is only supposition and extrapolation to arrive at a view that there IS a separate 'person' who is God, but not the Father. Considerable 'reading-in' is required to make a case for a Holy Spirit person. Certainly, some verses may lend themselves to such a conclusion, but only when read in isolation.
One scripture does not stand alone to deduce truth or doctrine, but must be included in a broad range of scripture to get the most authentic understanding.
The disciples had no problem understanding what the Holy Spirit was. They certainly didn’t make more of it than what they learnt from Jesus.
for the Holy Spirit will teach you in that very hour what you ought to say." Luke 12:12
for it will not be you speaking, but the Spirit of your Father speaking through you. Matthew 10:20
We see here the two terms used refer to the same thing. The HS is the power and presence of God. If we choose to make up a person we must ignore these verses to do it.
The HS -
- is never greeted, not sends greetings by/through any NT author.
- has no name. God names everything - all the stars, but not His spirit!
- proceeds from the Father - not God! John 15:26
- doesn't know basic things - in fact is oblivious to essential things Mark 13:32, Luke 10:22 ('no one knows the son except the Father')
- being called 'he' and 'him' is unwarranted in our bibles. Unless it is referring to God or the Father specifically, then 'He' etc would be appropriate. Matt 1:20 Heb 9:8
- when referred to as 'a' gift etc., 'it' or 'which' would be more appropriate. Acts 10:45, Luke 11:20
- needs some solid scriptural support for a 'person', hence 1 John 5:7 has been extended to supply that which God never intended. (even though now corrected in most bibles, some shamelessly or ignorantly still quote this)
- is missing from every vision of the throne whether Jesus is there or not. God is invisible, yet He is 'seen' there with His firstborn human son.
- is never taught by the Apostles to be a 'person', but is made dogma centuries after the church began.
There are many more examples of the HS being expressed as the power and presence of God, and now of Jesus also. Jesus is now expressed AS the spirit (1Cor 3:17) - being the essence of God in human form.
No, there is no need to see the Holy Spirit as distinct from the Father or God. 1 Cor 8:6 pronouncing the truth clearly and providing no reason at all to add another person to this dynamic duo of Father and son.
for us there is but one God, the Father, from whom all things came and for whom we live; and there is but one Lord, Jesus Christ, through whom all things came and through whom we live.
Are we to consider that the 'spirit of' truth, wisdom, Christ, etc are separate entities? Of course not. So why should the Spirit of God be separate from God the Father?
Therefore, since He (Jesus) has been exalted at the right hand of God, and has received the promise of the Holy Spirit from the Father, He has poured out this which you both see and hear. Acts 2:33
So there is no 'person', unless we make one up from poorly considered verses that are persuaded to fit the dogma - while ignoring all those that are quite clearly contrary and explicit in not making the Holy Spirit a person.
None of the verses cited by OP insist on a 'person', unless it is read-in.
John 14:26 for example has 'ho' - this is translated 'which' in most other places so the publishers bias has provided 'he' or 'whom'. This widespread use of personal pronouns confuses correct understanding.