Another nginx revproxy + rewrite + url mask

I know there's been a lot of posts about nginx + rewrite but I have a case where I cannot get it to work properly.

I have a multiple dockerized flask apps let's name it: vm1,vm2,vm3...vm6

I have a domain: manager.mydomain.com

What I'd like to achieve: when user navigates to https://manager.mydomain.com/vm6

gets redirected e.g to

https://manager.mydomain.com/vm6/login (and others endpoints /admin ....)

So generally speaking that is covered https://manager.mydomain.com/vm6/(.*) gets redirected to flask app. Unfortunately there are links that shall be rewritten as well.

My current trial:

http {

  upstream managervm4 {
    least_conn;
    server X.X.X.X:5004;
}

  upstream managervm6 {
    least_conn;
    server Y.Y.Y.Y:5006;
}

  server {

    server_name manager.mydomain.com;

    listen 443 ssl;

    ssl_certificate /etc/letsencrypt/live/manager.mydomain.com/fullchain.pem;
    ssl_certificate_key /etc/letsencrypt/live/manager.mydomain.com/privkey.pem;

    access_log /var/log/nginx/dtmanager.access.log;
    error_log /var/log/nginx/dtmanager.error.log;

    log_subrequest on;

    location /vm6 {
      rewrite ^/vm6$ https://manager.mydomain.com/vm6/ permanent;
    }


    location /vm6/ {
      #rewrite /vm6/(.*) /vm6/$1 break;
      sub_filter '"/' '"/vm6/';
      sub_filter_once off;
      proxy_pass http://managervm6/;
      #proxy_redirect off;
      proxy_set_header Host $host;
      proxy_set_header X-Real-IP $remote_addr;
      proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
      proxy_set_header X-Forwarded-Proto https;
    }
}

When I navigate curl -i https://manager.mydomain.com/vm6/admin I get in response:

Server: nginx/1.13.9
Date: Fri, 02 Jul 2021 09:14:40 GMT
Content-Type: text/html; charset=utf-8
Transfer-Encoding: chunked
Connection: keep-alive
Location: http://manager.mydomain.com/admin/

BUT if I navigate to curl -i https://manager.mydomain.com/vm6/login I get correct response, but then log-in does not work (I guess there's something wrong with redirections)

What am I doing wrong? Thanks!