Seems like the proper fix would be to introduce a <h> element with heading level dictated only by the number of <section> nesting. But it's too late for that now I guess.

Anyway, I'm quite surprised to learn all this about <h1> while I've always read everywhere up until today and including on MDN (Mozilla's documentation), that one should use only one <h1> per page.

Now I wonder if and how <section> nesting affects <h2>, <h3>, etc.