DY, do you mean anything different than my first, and main Pshat?
I think I should add that even without any Kasha this is the way I’d understand Tosafos.
A side point. There is an Hagaah changing the Ein Ruach Chachamim to Ruach Chachamim in the words of Rabbeinu Tam. There is no need to change it if you see the Tosafos in BB referenced in Massores Hashas. Rabbeinu Tam takes it for granted that there is another side to the coin.