Excellent analysis. The more I’ve watched the prequels the more I’ve noticed how much they add to the characters from the OT.
When he says “Failed I have” in Revenge of the Sith, he isn’t just talking about losing to Sidious in a duel, he’s talking about how he failed the galaxy because the Jedi Order lost its way.
Yoda’s leaving the battle with Sidious unfinished always bothered me but looking at it this way it starts to make more sense. Believing he’s already failed, he sees no reason to prolong the battle and risk the legacy of the Jedi dying with him.