For one thing, the mayor uses the low-class vernacular verb "ставить" referring to getting a shot of the vaccine; from the old substandard phrase "ставить прививку", which used to be criticized in Soviet textbooks. Which is fine, given his social history; but a news portal (does the eponymous newspaper still exist?) repeated his verb when they reported on his disclosure (1st paragraph), without changing the phrase into a more standard form. The disorienting effect of this, at least to me, is as if he has "supplied" the vaccine somewhere.
The blog post, which the article refers to, ends in a passage with another grammatical feature that feels relatively recent (10-15 years?) — a peculiar absence of the first-person pronoun in the second sentence:
I first started noticing this peculiar stinginess for pronouns in unsolicited emails from recruiters that I occasionally receive; then I noticed it in the rare Putin's speeches that I sometimes can't help but overhear; and I still can't figure out why this has taken off. It still sounds as a jarring stylistic novelty to me.