Example: The human owner of ERC20 wallet (X) owes the human owner of ERC20 wallet (Y) an amount of (T) ERC20.
Is there any function that the owner of Wallet (Y) can send a request message to the owner of Wallet (X) requesting the owed amount?
Welcome to SE! There is no method to "request" a payment from someone, mostly because the change would be done in that contract, and there is no way of "notifying" the involved party, especially if Y is a normal account address.
The current flows for ERC20 are:
approval by X, then transferFrom(X) by Y
transfer to Y by X
But the reverse has not been proposed in a widely adopted standard as of yet, mostly because of the "notification issue".
Hope that helps.