Thankfully, I haven't been working on this for a year :) But I finally had a spare gap to do a deep dive on this and have found that nginx doesn't cache responses that include the Set-Cookie header. Given Laravel authentication pipelines include Set-Cookie on every response you need to tell nginx to ignore those headers, your auth block needs to look something like this:
location = /m/auth {
internal;
proxy_pass http://laravel.local/auth;
proxy_pass_request_body off;
proxy_set_header Content-Length "";
proxy_set_header X-Original-URI $request_uri;
proxy_ignore_headers Set-Cookie; #this here
proxy_cache auth_cache;
proxy_cache_methods GET;
proxy_cache_valid 200 10m;
proxy_cache_key "$cookie_session";
}