IDK about Я, but Peter I definitely reshaped, along the European typesetting guidelines, some letters like lowercase a (which traditionally looked more like the Greek alpha, α), and most drastically the t (т) which for the best part of 17th century looked like Latin m. (This shape still remains in Cyrillic cursive.)
He didn't invent those shapes, though; just picked the preferred ones. In particular, the m/т distinction is still present across different Slavic scripts even in non-cursive form, because they standardized on different variants:
https://ru.wikipedia.org/wiki/%D0%A2_(%D0%BA%D0%B8%D1%80%D0%...
#/media/%D0%A4%D0%B0%D0%B9%D0%BB:Special_Cyrillics_BGDPT.svg){kind=link}
sometimes when I visit twitter, browser or whatever starts to think that Russian twits are actually Bulgarian, and this changes shape of some Cyrillic letters, making text looking somewhat funny to russian eye. T is one of them, IIRC.
Do you have a source on that? As a Bulgarian (where Cyrillic comes from) i had never heard anything of the like, and a short Google, in Bulgarian or Russian, found nothing.