It does also give the right solution, using an xml parser.

We don’t know the use case.

Maybe the questioner is also in full control of the HTML creation and they don’t need a parser for all possible HTML edge cases.

Maybe they are, but they would also need to ensure a well-defined subset of HTML and also show that the subset is a reglar (Chomsky Type 3) grammar.

It seems that even the very conceptually simple example given by the questioner is impossible.