How to configure NGINX to render pages correctly?

Question

Nginx

Good time!
After migrating the site from apache to nginx, any URL displays the content of the main page.
For example: site.com, site.com/page/, site.com/p_0Ljk
Installed NGINX, PHP-FPM, PHP7.2 I

suspect that the problem is the lack of some parameters in the NGINX config itself. I will be glad for any help. If not, please help and indicate what to fix to make the site work. Thanks in advance.
nginx config

server {
listen  01.23.45.67:443 ssl http2;
server_name  site.com www.site.com;
root  /home/user/workspace/sites/site.com;

if ($http_host ~ "^www\.(.*)$"){
set $http_host_1 $1;
rewrite ^(.*)$ https://$http_host_1/$1 redirect;
}

# ssl on;
ssl_certificate /etc/certs/user/site.com_10-07-2020_11:03:44_letencrypt.crt_v2;
ssl_certificate_key /etc/certs/user/site.com_10-07-2020_11:03:44_letencrypt.key;
#ssl_protocols TLSv1 TLSv1.1 TLSv1.2;
#ssl_ciphers  "HIGH:!RC4:!aNULL:!MD5:!kEDH";
ssl_protocols TLSv1 TLSv1.1 TLSv1.2 TLSv1.3;
ssl_ciphers TLS13-CHACHA20-POLY1305-SHA256:TLS13-AES-128-GCM-SHA256:TLS13-AES-256-GCM-SHA384:ECDHE:!COMPLEMENTOFDEFAULT;
ssl_prefer_server_ciphers on;

add_header Strict-Transport-Security 'max-age=604800';
access_log /etc/nginx/vhost_logs/site.com_access;
error_log /etc/nginx/vhost_logs/site.com_error;


location ~ /.well-known { allow all; }

# location ~* robots.txt  { root /etc/nginx; }

location ~ /\.ht {
deny all;
access_log off;
log_not_found off;
}

location / {

root /home/user/workspace/sites/site.com;
index index.php index.html index.htm;
if (!-e $request_filename) {
rewrite ^(.+)$ /index.php?q=$1 last;
}

}
location ~ \.php$ {
try_files $fastcgi_script_name =404;
root                       /home/user/workspace/sites/site.com;
#fastcgi_pass       localhost:9009;
fastcgi_pass unix:/var/run/php-fpm/php72w-user.sock;
include fastcgi_params;
fastcgi_split_path_info                 ^(.+?\.php)(/.*)?$;
fastcgi_index index.php;
fastcgi_param   SCRIPT_FILENAME         /home/user/workspace/sites/site.com$fastcgi_script_name;
fastcgi_param   PATH_TRANSLATED         /home/user/workspace/sites/site.com$fastcgi_script_name;

fastcgi_buffers 8 64k;
fastcgi_buffer_size 128k;
fastcgi_busy_buffers_size 128k;

fastcgi_connect_timeout 120;
fastcgi_read_timeout 900;
fastcgi_send_timeout 900;

fastcgi_cache off;
fastcgi_cache_key "$request_method|$http_if_modified_since|$http_if_none_match|$host|$request_uri";
fastcgi_cache_valid 200 10s;

limit_conn lfcgi 50;

#fastcgi_param   SCRIPT_FILENAME         /workspace/sites/site.com$fastcgi_script_name;
#fastcgi_param   PATH_TRANSLATED         /workspace/sites/site.com$fastcgi_script_name;

set             $path_info              $fastcgi_path_info;
fastcgi_param   PATH_INFO               $path_info;
}

# error_page  404              /404.html;
# location = /40x.html {
# }
# error_page   500 502 503 504  /50x.html;
# location = /50x.html {
# }
}

Answer 1

The .htaccess file, as it turned out, had the following rules:

RewriteRule ^page/([0-9]+)/$ index.php?page=$1 [L,QSA]
RewriteRule ^cat/([0-9]+)/(.*)/([0-9]+)/$ cat.php?id=$1&name=$2&page=$3 [L,QSA]
RewriteRule ^cat/([0-9]+)/(.*)/$ cat.php?id=$1&name=$2 [L,QSA]
RewriteRule ^collections/$ collections.php [L,QSA]
RewriteRule ^collections/([0-9]+)/$ collections.php?page=$1 [L,QSA]
RewriteRule ^search/(.*)/([0-9]+)/$ search.php?q=$1&page=$2 [L,QSA]
RewriteRule ^search/(.*)/$ search.php?q=$1 [L,QSA]

For Nginx, the rules will be:

rewrite ^/page/([0-9]+)/$ /index.php?page=$1 last;
rewrite ^/cat/([0-9]+)/(.*)/([0-9]+)/$ /cat.php?id=$1&name=$2&page=$3 last;
rewrite ^/cat/([0-9]+)/(.*)/$ /cat.php?id=$1&name=$2 last;
rewrite ^/collections/$ /collections.php last;
rewrite ^/collections/([0-9]+)/$ /collections.php?page=$1 last;
rewrite ^/search/(.*)/([0-9]+)/$ /search.php?q=$1&page=$2 last;
rewrite ^/search/(.*)/$ /search.php?q=$1 last;