How do Biblical Unitarians understand verses that appear to identify God (the Father) and the Holy Spirit as different beings/entities? Here are a few notable passages (the list is probably not exhaustive - edits are welcome):

13 So if you, despite being evil, know how to give good gifts to your children, how much more will your heavenly Father give the Holy Spirit to those who ask Him?” (Luke 11:13 NASB)


14 The grace of the Lord Jesus Christ, and the love of God, and the fellowship of the Holy Spirit, be with you all. (2 Corinthians 13:14 NASB)


26 But the Helper, the Holy Spirit whom the Father will send in My name, He will teach you all things, and remind you of all that I said to you. (John 14:26 NASB)


22 and the Holy Spirit descended upon Him in bodily form like a dove, and a voice came from heaven: “You are My beloved Son, in You I am well pleased.” (Luke 3:22 NASB)


33 Therefore, since He 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 NASB)


10 For to us God revealed them through the Spirit; for the Spirit searches all things, even the depths of God. 11 For who among people knows the thoughts of a person except the spirit of the person that is in him? So also the thoughts of God no one knows, except the Spirit of God. 12 Now we have not received the spirit of the world, but the Spirit who is from God, so that we may know the things freely given to us by God. 13 We also speak these things, not in words taught by human wisdom, but in those taught by the Spirit, combining spiritual thoughts with spiritual words. (1 Corinthians 2:10-13 NASB)

At face value, these verses appear to be addressing God (the Father) and the Holy Spirit as two separate beings/entities. How do Biblical Unitarians make sense of these and similar passages?
The issue of the Holy Spirit with Biblical Unitarianism is a bit different from Jesus.

&quot;Every use of “the Holy Spirit” and “holy spirit” can either be
explained as being a name for God or the name of the gift of God.&quot;
Appendix 6: Usages of &quot;Spirit&quot;

In some cases, then, for Biblical Unitarians, references to the 'holy spirit' are synonyms for 'God'. If it's the latter, though (the 'gift of God'), it is in some sense a different 'entity'.
For a more detailed discussion of this, see &quot;2) The “holy spirit” (lower case “h” and “s”) is the gift of God’s nature&quot; in Appendix 11: What is the Holy Spirit?.
I believe all the verses you reference are dealt with as this second sense - the gift of God's nature which transforms the recipient. For example, as pertains to Luke 3:22,

&quot;Jesus himself needed God’s gift of holy spirit to have supernatural
power, just as the leaders and prophets of the Old Testament did;
which is why God put holy spirit upon Jesus. God put holy spirit upon
Jesus immediately after he was baptized by John the Baptist (Matt.
3:16; Mark 1:9-10; Luke 3:21-22). This fulfilled the Old Testament
prophecies that God would put holy spirit upon the Messiah, enabling
him in his ministry (Isa. 11:2; 42:1; 61:1).&quot; (ibid.)

So the answer is yes, Biblical Unitarians would view the holy spirit as in some cases conceptually distinct from God ('the Father'), but in this sense the holy spirit isn't technically speaking God himself.