Ruach is translated (in the KJV) 232 times 'spirit', 90 times 'wind' and 28 times 'breath'. A few other times it is translated by other, similar, wordings.
Yom is translated 1,167 times 'day', 65 times as 'time' and, again, a smattering of other related terms otherwise.
Source - Young's Analytical Concordance.
There can be no doubt that the collocation means 'the spirit of the day' or 'the wind of the day' or 'the breath of the day'.
The previous mention of ruach is when the Spirit of God 'hovered' or 'fluttered' (YLT) over the face of the waters. This is activity but not progress.
A lot of exertion is required for birds that hover and some species are clearly gifted with special talent to do so, such as the kestrel. That they do so is usually a matter of focusing on that which is happening below them.
What was below was a darkness, an obscurity, which belied penetration. The depths held a secret that was dark, Genesis 1:1-5.
This secret comes to the fore when a serpentine spirit, Genesis 3:1, acts out of proper authority (the spirit acting in holiness had addressed the man not the woman, Genesis 2:16,17).
Once the woman is influenced unto deception, and once the man is influenced unto transgression, the 'voice of the Lord' . . . 'walks' in the 'spirit of the day'.
'Lord' 'voice' and 'spirit' : three designations.
The Lord, his word and his spirit.
And, now, progress. No longer hovering but in definite motion : 'walked'.
The 'wind of the day' happens in the cool of the evening and the KJV translators have expressed the practical idiom of the metaphor, not the spiritual interpretation. Understandably.
The day of rest is over.
Man has failed and is to be banished. Man has transgressed under temptation. The cherubim now appear, not attached to the first humanity. But 'God dwelleth the cherubim' ('between' is a mistranslation).
They are 'settled' at the furthest extremity of the garden, eastwards, awaiting the rising of the sun of a new day.
They shall be realised in another humanity - one that shall be promised as rising above the entity which brought sin into the world and (from above) bruising his head.
Ascension will achieve that.
But now, a patient waiting for the promised seed. A seed not of the man but of the woman.
Then the Sun of Righteousness, Malachi 4:2, shall arise and his beams (his 'wings') shall give healing. In the beauties of holiness, from the womb of the morning ; He has the dew of his youth, Psalm 110.
All of this is resplendent with spiritual truth and pregnant with heavenly meaning.