SSI is still a thing: I use it on my personal website. It isn't really part of the HTML, though: it's a server-dependent extension to HTML. It's supported by Apache and nginx, but not by every server, so you have to have control over the server stack, not just access to the documents.
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Or, better, "Server Side Includes" (SSI): https://en.wikipedia.org/wiki/Server_Side_Includes
SSI is still a thing: I use it on my personal website. It isn't really part of the HTML, though: it's a server-dependent extension to HTML. It's supported by Apache and nginx, but not by every server, so you have to have control over the server stack, not just access to the documents.