Continuing a narrative about tanya being “torah shebichsav” or whatever is just that – a narrative. You have no evidence that chabad ever looked at it that way before the last rebbe changed everything.
As for the igeres. Did you notice that he’s talking to working people? You left out the first part of the letter. He’s cautioning them to work and have families leshem shomayim.
For them, he’s saying that what will bring the geulah is mitzvos maasios in addition to their learning (he says gam kein), tzedaka being a prime example.
He’s coming laafukei the idea that all you have to do is learn, because lots of people think that way. Also, why do chessed if chazal say that torah is bigger?
He’s saying that in our time, ikvesa demishicha, they need physical involvement too(train the words ‘gam kein’)
And clearly, the baal hatanya didn’t spend all of his time or even most of his time doing chessed; he sat and learned all day, and was a massive talmid chochom.