Just asking (2): does “worship in spirit and truth” have anything to do with “born of the Spirit”?

I’ve always wondered.    
Is it a capital S or just s?

A little sample in John 4:23-24 tells the picture, and magnifies the uncertainties:

Yet a time is coming and has now come when the true worshipers will worship the Father in the Spirit and in truth, for they are the kind of worshipers the Father seeks. God is spirit, and his worshipers must worship in the Spirit and in truth.” (NIV)

But the time is coming—indeed it’s here now—when true worshipers will worship the Father in spirit and in truth. The Father is looking for those who will worship him that way. For God is Spirit, so those who worship him must worship in spirit and in truth.” (NLT)

But a time is coming—and now is here—when the true worshipers will worship the Father in spirit and truth, for the Father seeks such people to be his worshipers. God is Spirit, and the people who worship him must worship in spirit and truth.” (NET)

時候將到，現在就是了，那真正敬拜父的，要用心靈和誠實敬拜他，因為父要這樣的人敬拜他。上帝是靈，所以敬拜他的必須用心靈和誠實敬拜他。」《和修》

但時候將到，現在就是了，真誠敬拜的人要以靈以真理*敬拜父，因為父正尋找這樣敬拜他的人。神是靈，敬拜的人必須以靈以真理來敬拜。」（腳註*4:23 以靈以真理：「靈」在這裏可以是指聖靈。神是靈［24節〕，必須是在聖靈裏的人才能進到神面前。而「真理」更可能是指主耶穌基督［14:6〕。）《新漢語譯本》

然而有一個時刻就要來到，現在就是了，那靠聖靈按真理敬拜父的，才是真正敬拜的人；因為父想要這樣的人來敬拜他。神是靈，敬拜他的必須靠聖靈按真理敬拜他。《環球聖經譯本》

I’m just asking: is it with the Holy Spirit, or just with the heart inside (spirit) as opposed to liturgy outside?

I’ve already dropped asking if it is sincerity or truth (Truth)!

Versions, English or Chinese, are no help.
Would context be?

In the preceding chapter Jesus discussed with Nicodemus the notion of “being born again (above)”:

Jesus answered, “Very truly I tell you, no one can enter the kingdom of God unless they are born of water and the Spirit. Flesh gives birth to flesh, but the Spirit gives birth to spirit. You should not be surprised at my saying, ‘You must be born again.’ The wind blows wherever it pleases. You hear its sound, but you cannot tell where it comes from or where it is going. So it is with everyone born of the Spirit.” (John 3:5-8 [NIV])

Here clearly the Holy Spirit is in view.

Then towards the end of the chapter:
For the one whom God has sent speaks the words of God, for God gives the Spirit without limit. (John 3:34 [NIV])

That is the final time Spirit is mentioned, before Chapter 4.

Shouldn’t the same referent continue in Chapter 4?
Shouldn’t “worship in Spirit” be in view to indicate the nature of those is “born of the Spirit”, i.e. “born again (above)”?

And what about “worship in Spirit and truth” is better rendered “worship in Spirit, that is Truth”?
Doesn’t Jesus refer to “the Spirit of Truth” (John 14:16-17 [NIV])?

I’m just asking.