Wrong page shown on post request

The plugin shouldn’t be showing a cached page for a POST request. Enable the debug log for your IP and POST again and check what the plugin does. It should say it’s not using the cache.

Was that debug log from a request for the main page? If not, then what URL was it? Was it the POSTing to https://geriartriya.ru/rg/simferopol/chastnye-pansionaty-simferopol ? There’s definitely something up with your server then. Line 125 of wp-cache-phase1.php will stop the plugin serving a cached page to a POST request.

if ( ! $cache_enabled || ( isset( $_SERVER['REQUEST_METHOD'] ) && in_array( $_SERVER['REQUEST_METHOD'], array( 'POST', 'PUT', 'DELETE' ) ) ) || isset( $_GET['customize_changeset_uuid'] ) ) {
    return true;
}

Do you have some sort of proxy running that might interfere with the real URL seen by WordPress?

If that line is returning true then it can’t be serving a cached file as the file is served by the function wp_cache_serve_cache_file() that is called afterwards in wp-cache-phase1.php

I’m sorry, I don’t know why this happens on your site. You could go into the get_current_url_supercache_dir function and examine what directory it returns. Use error_log() and examine your PHP error_log. Maybe you’ll find something there that will help.