Hi, kotrya.
Thank you for reaching out on the Apple Support Communities. We understand that you aren’t able to search for new music using your Apple Music subscription after updating to macOS Catalina. However, it sounds like you’re able to search for content in the iTunes Store. It also appears that you’ve done some great troubleshooting in checking your subscription and ability to access other aspects of your Apple Music.
We suggest checking the Date & Time to make sure it is set correctly. An incorrect reading here can cause issues with accessing some of the Apple servers. (System Preferences > Date & Time)
Then download and run a Malwarebytes scan. Make sure to remove or quarantine any threats and restart your Mac. They have a free version you can download from their website:
Malwarebytes Cybersecurity for Home and Business | Malwarebytes
Finally, check to see if you have any profiles installed that may be interfering with your connection. If you have a profile installed, you’ll find it at System Preferences > Profiles.
Cheers.