Apache has supported Server Side Includes forever. All you need to do is drop an 'include' in your HTML file and Apache will inject the contents in the right place.
<!--#include virtual="/header.html" -->
I don't know for certain but suspect other webservers will have similar functionality.https://httpd.apache.org/docs/current/howto/ssi.html
Edit:
IIS: https://docs.microsoft.com/en-us/iis/configuration/system.we...
Lighttpd: https://redmine.lighttpd.net/projects/1/wiki/docs_modssi
Nginx: https://nginx.org/en/docs/http/ngx_http_ssi_module.html
Tomcat: https://tomcat.apache.org/tomcat-7.0-doc/ssi-howto.html