Hey there @Lostoniy,
Thanks for posting and welcome to the Community!
We get that you're not able to have synchronization between your Spotify desktop app and Discord. As everything seems to work fine on your mobile, please make sure that the desktop app is not using a different Spotify account from the one you have logged in you mobile. You can also doublecheck the information about connecting your Discord with Spotify here.
Also, here on Discord's official page you can find more additional info on the topic.
Hope you find this useful. Keep us posted if you have any questions.
Help others find this answer and click "Accept as Solution".
If you appreciate an answer, maybe give it a Like.