One modern approach would be Caddy Server's templates, using Golang templating:

https://caddyserver.com/docs/modules/http.handlers.templates

The "include" function should do the job:

{{include "path/to/file.html"}}

httpd, nginx, a number of other servers support SSI

https://nginx.org/en/docs/http/ngx_http_ssi_module.html

Caddy chose not to, I guess?

https://caddy.community/t/caddy-update-on-ssi-server-side-in...

You generally can’t use SSI on many popular platforms for static websites like Netlify, etc.

However, you could generate the static HTML easily and then publish it on those platforms, which is what many people do today (probably not often using SSI).