The key word in this question strikes me as being the word "subtle". If it is ignored, then answers will deal with whether 2 Corinthians 6:16 is a reference to the Holy Spirit's deity, or not. Yet, if the reference is subtle, then focus might need to go on how to find the evidence, when it is not clearly obvious.
A gentle unpicking of threads would be required if there's something subtle going on here. The first thread would be found in Leviticus, as the text in question is partially quoting this ancient statement of God, to the newly formed nation of Israel. God makes this promise to them:
"And I will set my tabernacle among you: and my soul shall not abhor
you. I will walk among you, and will be your God, and ye shall be my
people." Deuteronomy 26:11-12 A.V.)
There is no mention of the Holy Spirit here, but of God himself walking among them. The presence of God is linked to the tabernacle of God, in the camp of the Israelites. Of course, they all knew that they would not see God himself, with their eyes, moving throughout the camp. So, why did Paul quote this when warning Christians of the need to touch nothing unclean in order to have God receive them as his children? That is the context of the letter as illustrated by the preceding verses:
"Be ye not unequally yoked together with unbelievers: for what
fellowship hath righteousness with unrighteousness? and what communion
hath light with darkness? And what concord hath Christ with Belial? or
what part hath he that believeth with an infidel?" 2 Corinthians
Then comes the verse you quote, which is clearly a continuation of that line of questioning - getting Christians to see that they must not contaminate themselves with idolatry if God is to "dwell in them, and walk in them". That was exactly the point the Israelites had to get, having come out of the idolatry of Egypt. If God would tabernacle in their midst, they had to eschew all idolatry and remain clean, both spiritually and physically. Leviticus 26:1-13 details all of that, and
that is why Paul quoted that ancient text, first stated to the Israelites.
So far, there seems to be nothing of the Holy Spirit in this, let alone his deity. But that is why it is correct to include 1 Corinthians 3:16 alongside 2 Corinthians 6:16, which most Bibles with margins do, and which you did:
"Do you not know that you are the temple of God and that the Spirit of
God dwells in you?"
There is the subtle link. The temple / tabernacle of God as opposed to the temple of idols; Christians are the temple of God; he tabernacles (dwells) in them via the Spirit of God. And in the new testament, the Spirit of God is simultaneously called the Spirit of Christ, so that the 'clincher' verse is this one:
"But ye are not in the flesh, but in the Spirit, if so be that the
Spirit of God dwell in you. Now if any man have not the Spirit of
Christ, he is none of his. And if Christ be in you, the body is dead
because of sin: but the Spirit is life because of righteousness. But
if the Spirit of him that raised up Jesus from the dead dwell in you,
he that raised up Christ from the dead shall also quicken your mortal
bodies by his Spirit that dwelleth in you." Romans 8:9-11
Those who personally know, by experience, what Romans chapter 8 is on about, know that the Spirit indwelling them is simultaneously the Spirit of God and the Spirit of Christ, who communicates the life of God and Christ to them. This assures them that Father, Son and Holy Spirit are, as one, tabernacling within their bodies which have become temples of the living God.
Those who do not personally know, by experience, the outworking of Romans chapter 8, could not possibly be expected to make the subtle connection between it and 2 Corinthians 6:16. The subtlety of the hints of the Holy Spirit's deity in those scriptures, indeed, in all the scriptures, will be missed, for this is a matter of divine revelation given by the Holy Spirit himself.