After researching this very topic earlier; SSI is the most pragmatic solution. Check out Caddy's Template Language (based on Go), it is quite capable and quite similar to building themes in Hugo. Just much more bare bones.

I have built several sites with pure HTML+CSS, sprinkled with some light SSI with Caddy, and it is rock solid and very performant!

That's mentioned in TFA under "old school web server directives".