proxy_buffer_size 256k;

That size is huge and won't do you good. You can read the guide on how to tune it properly with one important note: fastcg_buffer_size and proxy_buffer_size are essentially the same thing, they are just applied to different upstream module of NGINX.

• proxy_buffer_size is the buffer for header of HTTP response of NGINX's proxy module
• fastcgi_buffer_size is the buffer for header of HTTP response of NGINX's fastcgi module

Because it is a header, it makes little sense to put things like 256k for that buffer because even a complete page HTML will hardly reach that size.

When you enable Varnish, Magento code will indeed output more HTTP headers, specifically X-Magento-Tags may be very large depending on catalog size and if looking at a category page.

For this you need to adjust both proxy_buffer_size and fastcgi_buffer_size. Why is because in your setup NGINX uses both modules: it proxies requests to Varnish (TLS termination), and does FastCGI communication to PHP-FPM.

So aside from tuning proxy_buffer_size, you need to do the same for fastcgi_buffer_size and tune it up as needed. You can either do this alongside fastcgi_ directives in /var/www/example.com/html/nginx.conf.sample or add this globally, e.g. /etc/nginx/conf.d/custom.conf and make sure it is loaded from nginx.conf.

Don't forget to tune *_busy_buffers_size as well as per the guide. E.g.:

fastcgi_buffer_size 16k;
fastcgi_busy_buffers_size 16k;

proxy_buffer_size 256k;

That size is huge and won't do you good. You can read the guide on how to tune it properly with one important note: fastcg_buffer_size and proxy_buffer_size are essentially the same thing, they are just applied to different upstream modules of NGINX.

• proxy_buffer_size is the buffer for header of HTTP response of NGINX's proxy module
• fastcgi_buffer_size is the buffer for header of HTTP response of NGINX's fastcgi module

Because it is a header, it makes little sense to put things like 256k for that buffer because even a complete page HTML will hardly reach that size.

When you enable Varnish, Magento code will indeed output more HTTP headers, specifically X-Magento-Tags may be very large depending on catalog size and if looking at a category page.

For this you need to adjust both proxy_buffer_size and fastcgi_buffer_size. Why is because in your setup NGINX uses both modules: it proxies requests to Varnish (TLS termination), and does FastCGI communication to PHP-FPM.

So aside from tuning proxy_buffer_size, you need to do the same for fastcgi_buffer_size and tune it up as needed. You can either do this alongside fastcgi_ directives in /var/www/example.com/html/nginx.conf.sample or add this globally, e.g. /etc/nginx/conf.d/custom.conf and make sure it is loaded from nginx.conf.

Don't forget to tune *_busy_buffers_size as well as per the guide. E.g.:

fastcgi_buffer_size 16k;
fastcgi_busy_buffers_size 16k;