why did u write $path: and not $path= in your first function code?
Wait forget it, you have to privde the relative path, you’re providing the full path.. When using load_plugin_textdomain, you gotta use your plugin folder + your language files folder only; so if your language files are inside wp-content/plugins/your-plugin/languages, use
load_plugin_textdomain( 'your-plugin', false, 'your-plugin/languages' );
When I do it like this with my plugins translations always work. And I remember that whenever translations of my plugins didn’t work, the wrong path was the problem in most of the cases.