Berachot 50a: נברך שאכלנו משלו and the meaning of ש

On Berachot 50a:

אמר רבי יוחנן נברך שאכלנו משלו הרי זה ת"ח למי שאכלנו משלו הרי זה בור

Or, in English:

R' Johanan says: If one says 'let us bless Him of whose bounty we have partaken' he shows himself a scholar; if he says 'Let us bless the one of whose bounty we have partaken', he shows himself an ignoramus.¹¹

What is the distinction between sheachalnu and lemi sheachalnu? Is it simply nuance in Mishnaic Hebrew, that the lemi when implied only connotes Hashem?

Rashi writes:

נברך שאכלנו משלו - משמע שהוא יחידי שהכל אוכלים משלו:

למי שאכלנו משלו - משמע מרובים הן זה זן את זה וזה זן את זה ולפי דבריו מברך את בעל הבית:

That is, lemi means that there are actually many who are zan, in which case the implication is to the host.

I would suggest that the prefix ש, which is short for אשר, has two functions, "whose" and "because." When we say נברך שאכלנו משלו, we are not saying 'let us bless Him of whose bounty we have partaken'. Rather, we are saying 'let us bless, because we have eaten of His." If so, the reference is to God, who we bless. However, if we say נברך למי שאכלנו משלו, then we are selecting the meaning of "whose". It is 'let us bless to He/he whose bounty we have partaken'. The word lemi forces ש to mean whose. And this is not the meaning of the statement. Or with this selected meaning, the referent is then ambiguous, as it can refer to the host.