[Null-Set]

The name of this feature is transclusion.

https://en.wikipedia.org/wiki/Transclusion

It was part of Project Xanadu, and originally considered to be an important feature of hypertext.

Notably, mediawiki uses transclusion extensively. It sometimes feels like the wiki is the truest form of hypertext.

[jes5199]

Ward Cunningham (inventor of the Wiki) spent some time trying to invent a transclusion-first wiki, where everyone had their own wiki-space and used transclusion socially https://en.wikipedia.org/wiki/Federated_Wiki

it never quite took off

[PaulHoule]

I think true transclusion would be more than that.

In Xanadu you could transclude just an excerpt from one document into another document.

If you wanted to do this with HTML you need an answer for the CSS. In any particular case you can solve it, making judgements about which attributes should be consistent between the host document, the guest document and the guest-embedded-in-host. The general case, however, is unclear.

For a straightforward <include ...> tag the guest document is engineered to live inside the CSS environment (descendant of the 3rd div child of a p that has class ".rodney") that the host puts it in.

Another straightforward answer is the Shadow DOM which, for the most part, lets the guest style itself without affecting the rest of the document. I think in that case the host can still put some styles in to patch the guest.