@fantasai unfortunately not.
Any new rel usage must be a whole URL->URL semantic.
A heading linking to itself with rel=self would look like the page is asserting that that heading fragment is also the whole page, which is not true, unless perhaps you use it on a singular top level H1, which should not link to itself anyway because it is confusing (bad for UX and a11y).
Scoped rel use in practice only for backcompat for rel=bookmark, maybe some rel=tag.