> E.g. expanding "t" to "the" seems like a no-brainer, just like "st" to "something". Is there a minimal set of, say, 200-500 of these that could simply be turned into a "standard keyboard" that everyone could learn?

Take a look at Evans Basic English Code, a shorthand system based off of Phillips Code (for telegraphs). It's a little dated, but the most common words are quite useful for writing or typing.

https://archive.org/details/evansbasicenglis00evan

(use the pdf, the txt file is a bad OCR and practically useless)

Also useful:

https://en.m.wikipedia.org/wiki/Most_common_words_in_English