missing opentelemetry headers on auth_request location

Describe your environment
EKS 1.24
Nginx:

nginx version: nginx/1.21.6
built by gcc 12.2.1 20220924 (Alpine 12.2.1_git20220924-r4)
built with OpenSSL 3.0.8 7 Feb 2023
TLS SNI support enabled
configure arguments: --prefix=/usr/local/nginx --conf-path=/etc/nginx/nginx.conf --modules-path=/etc/nginx/modules --http-log-path=/var/log/nginx/access.log --error-log-path=/var/log/nginx/error.log --lock-path=/var/lock/nginx.lock --pid-path=/run/nginx.pid --http-client-body-temp-path=/var/lib/nginx/body --http-fastcgi-temp-path=/var/lib/nginx/fastcgi --http-proxy-temp-path=/var/lib/nginx/proxy --http-scgi-temp-path=/var/lib/nginx/scgi --http-uwsgi-temp-path=/var/lib/nginx/uwsgi --with-debug --with-compat --with-pcre-jit --with-http_ssl_module --with-http_stub_status_module --with-http_realip_module --with-http_auth_request_module --with-http_addition_module --with-http_geoip_module --with-http_gzip_static_module --with-http_sub_module --with-http_v2_module --with-stream --with-stream_ssl_module --with-stream_realip_module --with-stream_ssl_preread_module --with-threads --with-http_secure_link_module --with-http_gunzip_module --with-file-aio --without-mail_pop3_module --without-mail_smtp_module --without-mail_imap_module --without-http_uwsgi_module --without-http_scgi_module --with-cc-opt='-g -O2 -fPIE -fstack-protector-strong -Wformat -Werror=format-security -Wno-deprecated-declarations -fno-strict-aliasing -D_FORTIFY_SOURCE=2 --param=ssp-buffer-size=4 -DTCP_FASTOPEN=23 -fPIC -I/root/.hunter/_Base/d45d77d/aab92d8/3b7ee27/Install/include -Wno-cast-function-type -m64 -mtune=generic' --with-ld-opt='-fPIE -fPIC -pie -Wl,-z,relro -Wl,-z,now -L/root/.hunter/_Base/d45d77d/aab92d8/3b7ee27/Install/lib' --user=www-data --group=www-data --add-module=/tmp/build/ngx_devel_kit-0.3.1 --add-module=/tmp/build/set-misc-nginx-module-0.33 --add-module=/tmp/build/headers-more-nginx-module-0.33 --add-module=/tmp/build/ngx_http_substitutions_filter_module-b8a71eacc7f986ba091282ab8b1bbbc6ae1807e0 --add-module=/tmp/build/lua-nginx-module-0.10.21 --add-module=/tmp/build/stream-lua-nginx-module-0.0.11 --add-module=/tmp/build/lua-upstream-nginx-module-8aa93ead98ba2060d4efd594ae33a35d153589bf --add-module=/tmp/build/nginx_ajp_module-fcbb2ccca4901d317ecd7a9dabb3fec9378ff40f --add-dynamic-module=/tmp/build/nginx-http-auth-digest-1.0.0 --add-dynamic-module=/tmp/build/nginx-influxdb-module-5b09391cb7b9a889687c0aa67964c06a2d933e8b --add-dynamic-module=/tmp/build/nginx-opentracing-0.19.0/opentracing --add-dynamic-module=/tmp/build/ModSecurity-nginx-1.0.3 --add-dynamic-module=/tmp/build/ngx_http_geoip2_module-a26c6beed77e81553686852dceb6c7fdacc5970d --add-dynamic-module=/tmp/build/ngx_brotli

Using the version: registry.k8s.io/ingress-nginx/opentelemetry:v20230312-helm-chart-4.5.2-28-g66a760794@sha256:40f766ac4a9832f36f217bb0e98d44c8d38faeccbfe861fbc1a76af7e9ab257f when i set a auth location like:

location = /auth {
    internal;

    opentelemetry on;
    opentelemetry_propagate;
    opentelemetry_trust_incoming_spans on;
    proxy_pass http://authorizer;
}
location / { 
    opentelemetry on;
    opentelemetry_propagate;
    opentelemetry_trust_incoming_spans on;
    
    auth_request  /auth;
    proxy_pass    http://application;
}

The open telemetry headers are available only for the location / backend but not for the location /auth backend.

What is the expected behavior?
I want to have the same trace id in both backends: (application and authorizer)

What is the actual behavior?
I have only the trace id generated for the application, but the open telemetry headers are not sent to the authorizer app.

Reproduce the report with the shown Nginx configuration, focusing on the location = /auth and location / blocks and the auth_request entry point. Compare the headers received by the authorizer and application backends; done means both receive headers carrying the same trace ID.