nginx - add header on html document only

Question

Goal:

Configure nginx to add a header only on html document without .html extension

Prerequisite:

Add a .html to documents is not possible (they are dynamically generated by another tool via proxy_pass) and they can't be served with .html

What I have tried:

• add_header directive alone is working but put the header on all resources (css, js, etc.).

• in server context :

if ($sent_http_content_type ~ "(text/html)") {
    add_header Link '<https://example.com>; rel="preconnect"';
}

• in http context :

map $sent_http_content_type $link_value {
    text/html '<https://example.com>; rel="preconnect"';
}
add_header Link $link_value;

but none works. I must be wrong with syntax or context...

Someone know how to make it works?