when uwsgi all process is busy, how to redirect?

Question

I'm currently using nginx + uwsgi + flask.
I'm using SSE from flask to get real time message from server to client (like one way socket). but, since I set process = 10, only 10 connection can be made.
once all process is busy, the new connect is hanging, and then got error (like net::ERR_NETWORK_CHANGED). and this will break all other connection in the process with this error

SIGPIPE: writing to a closed pipe/socket/fd (probably the client disconnected) on request /stream  !!!
uwsgi_response_write_body_do(): Broken pipe [core/writer.c line 429] during GET /stream 
OSError: write error
Client disconnected.

I want to show waiting page if all process is busy. I've been trying to solve this issue, but I'm really hard for me...

[uwsgi]
vhost=true
chdir=/Server/
#venv=/Server/venv
module = app:app
callable = application
master = true
processes = 10
socket = /tmp/uwsgi.sock
; http-socket = 0.0.0.0:8000
chmod-socket = 666
vacuum = true
die-on-term = true
enable-threads = true
wsgi-file = /Server/wsgi.py
;pythonpath = /Server/venv/lib/python3.10
logto = /Server/uwsgi.log
log-reopen = true
listen = 10  # No additional connections will be queued

# Increase timeouts
socket-timeout = 3600
harakiri = 3600
http-timeout = 3600

# Optional: Adjust buffer size if needed
buffer-size = 65535

this is my uwsgi.ini file.

server {
  listen 80;

  client_max_body_size 50M;

  location / {
    include uwsgi_params;
    uwsgi_pass unix:/tmp/uwsgi.sock;  # Use the uWSGI socket

    uwsgi_read_timeout 600;
    uwsgi_send_timeout 600;
    uwsgi_connect_timeout 60;
    proxy_buffering off;
    proxy_set_header Connection '';
    proxy_http_version 1.1;
    chunked_transfer_encoding off;
    proxy_cache off;


    # CORS settings
   # add_header 'Access-Control-Allow-Origin' '*' always;
   # add_header 'Access-Control-Allow-Methods' 'GET, POST, OPTIONS' always;
   # add_header 'Access-Control-Allow-Headers' 'Authorization, Origin, X-Requested-With, Content-Type, Accept' always;

    # Handle OPTIONS requests
    #if ($request_method = 'OPTIONS') {
    #    add_header 'Access-Control-Allow-Origin' '*';
    #    add_header 'Access-Control-Allow-Methods' 'GET, POST, OPTIONS';
    #    add_header 'Access-Control-Allow-Headers' 'Authorization, Origin, X-Requested-With, Content-Type, Accept';
    #    return 204;
    #}


    

    error_page 403 502 503 504 /error.html;
    proxy_intercept_errors on;
    
    proxy_next_upstream error timeout invalid_header http_503;
    proxy_next_upstream_tries 1;
  }


  location = /error.html {
    root /Server/static;
    internal;
  }
}

and this is my nginx default.conf.

so, I have 2 questions.

1. how can I redirect to waiting page, if all process is busy?
2. even if hanging request return fail (like timeout), how to keep alive all the other processes.

please help me T^T