If the Vedas are said to be of divine origin (did not come from any ordinary being), why does the Rig Veda say this “asmA idu stomaM saM hinomi rathaM na taSTeva” – “Similar to how a carpenter constructs a chariot, so have I created this for him”? How to interpret this?

The Veda itself says in many instances that it has created the Vedas. It means that it has illuminated the Vedas that already exist.
When one says that a carpenter makes a chariot, it does not mean that the carpenter created the tree/wood. He machines the wood that already exists and makes an object. Similarly, Permal has given the Vedas that already exist in a proper format.
Notes
The Vedas that were in a certain format during a previous kalpam are presented in the same format during the next kalpam by Bhagavan.
At the time of universal dissolution (Pralaya kalam) when only the Bhagavan exists and everything else is destroyed, Bhagavan preaches the Vedas during the kalpa that follows in the same format that the Vedas were in during the previous kalpa. That is why the Vedas are called Apaurusheyam, of divine origin.