how to set up websocket server along with two laravel backend and a spa

i have two laravel backend setup on different routes. and there is a spa on root. now i want to set a websocket server along with it. here is my website.conf

############## block-4 : multiple subdirectory testing ############
server {
    listen 80;
    #    server_name abc.xyz;
    server_name _;
    root /var/www/html/abc.xyz;
    #    root /var/www/html;

    add_header X-Frame-Options "SAMEORIGIN";
    add_header X-Content-Type-Options "nosniff";

    index index.html index.php;

 
    location / {
        # root /var/www/html/abc.xyz;
        try_files $uri  /index.html ;
    }

    charset utf-8;

    location = /favicon.ico {
        access_log off; log_not_found off;
    }
    location = /robots.txt {
        access_log off; log_not_found off;
    }

    # error_page 404 /index.php;

############## block-4 : multiple subdirectory testing ############
server {
    listen 80;
    #    server_name abc.xyz;
    server_name _;
    root /var/www/html/abc.xyz;
    #    root /var/www/html;

    add_header X-Frame-Options "SAMEORIGIN";
    add_header X-Content-Type-Options "nosniff";

    index index.html index.php;

 
    location / {
        # root /var/www/html/abc.xyz;
        try_files $uri  /index.html ;
    }

    charset utf-8;

    location = /favicon.ico {
        access_log off; log_not_found off;
    }
    location = /robots.txt {
        access_log off; log_not_found off;
    }

    # error_page 404 /index.php;

    # BACKEND location rewrite instructions
    location /backend {
        alias /var/www/html/abc.xyz/backend;

        try_files $uri $uri/ @backend;

        location ~ \.php$ {
            include fastcgi_params;
            fastcgi_param SCRIPT_FILENAME $request_filename;
            fastcgi_pass unix:/var/run/php/php8.0-fpm.sock;
        }
    }

    location @backend {
        # rewrite /backend/(.*)$ /backend/index.php?/$1 last;
        rewrite ^/backend/(.*)$ /backend/index.php last;
    }
    # end of the BACKEND location


    # BACKEND location rewrite instructions
    location /api {
        alias /var/www/html/abc.xyz/api;

        try_files $uri $uri/ @api;

        location ~ \.php$ {
            include fastcgi_params;
            fastcgi_param SCRIPT_FILENAME $request_filename;
            fastcgi_pass unix:/var/run/php/php8.0-fpm.sock;
        }
    }

    location @api {
        rewrite /api/(.*)$ /api/index.php?/$1 last;
    }
    # end of the BACKEND location


    #  phpmyadmin rewrite rules.
    location /phpmyadmin {
        root /usr/share/;
        index index.php index.html index.htm;
        location ~ ^/phpmyadmin/(.+\.php)$ {
            try_files $uri =404;
            root /usr/share/;
            fastcgi_param SCRIPT_FILENAME $request_filename;
            fastcgi_pass unix:/var/run/php/php8.0-fpm.sock;
            fastcgi_index index.php;
            include /etc/nginx/fastcgi_params;
        }

        location ~* ^/phpmyadmin/(.+\.(jpg|jpeg|gif|css|png|js|ico|html|xml|txt))$ {
            root /usr/share/;
        }
    }
    # end of phpmyadmin block here.

    # web socket configuration here 
  location /ws* {
    proxy_pass             http://127.0.0.1:6001;
    proxy_set_header Host  $host;
    proxy_read_timeout     60;
    proxy_connect_timeout  60;
    proxy_redirect         off;

    # Allow the use of websockets
    proxy_http_version 1.1;
    proxy_set_header Upgrade $http_upgrade;
    proxy_set_header Connection 'upgrade';
    proxy_set_header Host $host;
    proxy_cache_bypass $http_upgrade;
  }
    # end of websocket configuration


    location ~ /\.(?!well-known).* {
        deny all;
    }
}

############# end block-4 ######################

the location /ws block is taken from laravel websockets documentation. but this location block is giving 404 not found error. but this nginx configuration doesn't work. My laravel website project works fine on localhost.

edit

this is the output of lsof -i :80,443,6001

COMMAND    PID     USER   FD   TYPE  DEVICE SIZE/OFF NODE NAME
php     414490     root    5u  IPv4 5974385      0t0  TCP *:x11-1 (LISTEN)
php     414490     root    6u  IPv4 5991457      0t0  TCP localhost.localdomain:x11-1->localhost.localdomain:35684 (ESTABLISHED)
nginx   415533     root    6u  IPv4 5990824      0t0  TCP *:https (LISTEN)
nginx   415533     root    7u  IPv4 5990825      0t0  TCP *:http (LISTEN)
nginx   415534 www-data    6u  IPv4 5990824      0t0  TCP *:https (LISTEN)
nginx   415534 www-data    7u  IPv4 5990825      0t0  TCP *:http (LISTEN)
nginx   415535 www-data    6u  IPv4 5990824      0t0  TCP *:https (LISTEN)
nginx   415535 www-data    7u  IPv4 5990825      0t0  TCP *:http (LISTEN)
nginx   415536 www-data    6u  IPv4 5990824      0t0  TCP *:https (LISTEN)
nginx   415536 www-data    7u  IPv4 5990825      0t0  TCP *:http (LISTEN)
nginx   415537 www-data    6u  IPv4 5990824      0t0  TCP *:https (LISTEN)
nginx   415537 www-data    7u  IPv4 5990825      0t0  TCP *:http (LISTEN)
nginx   415538 www-data    6u  IPv4 5990824      0t0  TCP *:https (LISTEN)
nginx   415538 www-data    7u  IPv4 5990825      0t0  TCP *:http (LISTEN)
nginx   415539 www-data    6u  IPv4 5990824      0t0  TCP *:https (LISTEN)
nginx   415539 www-data    7u  IPv4 5990825      0t0  TCP *:http (LISTEN)
nginx   415539 www-data    8u  IPv4 5985866      0t0  TCP linux:https->157.42.56.21:55728 (ESTABLISHED)
nginx   415539 www-data   12u  IPv4 5985868      0t0  TCP localhost.localdomain:35684->localhost.localdomain:x11-1 (ESTABLISHED)