Music.app will not launch in catalina

First boot into Safe Mode (How to use safe mode on your Mac - Apple Support) by booting with the Shift key held down and check there to see if the problem persists.  Reboot normally and test again.

NOTE: Safe Mode boot can take up to 10 minutes as it's doing some system cache cleaning, volume verifying and directory repairing. 

It if still won't launch download and reapply the macOS Catalina 10.15.5 Combo Update.  It will reinstall the system and Apple apps, including Music.

Log into another user account, Set up users, guests, and groups on Mac,  and see if the problem persists. (This tells us if the problem is limited to your user account or is system wide).

If the problem is limited to your user account then in your user account download and run Etrecheck. Etrecheck is a diagnostic tool that was developed by one of the most respected users here in the ASC and recommended by Apple Support  to provide a snapshot of the system and help identify the more obvious culprits that can adversely affect a Mac's performance.

Copy the report

and use the Add Text button to include the report in your reply. How to use the Add Text Feature When Posting Large Amounts of Text, i.e. an Etrecheck Report

IMPORTANT:

Before running Etrecheck assign Full Disk Access to Etrecheck in the Etrecheck's Privacy preference pane so that it can get additional information from the Console and log files for the report:

Also click and read the About info to further permit full disk access.

Then we can examine the report and see if we can determine what might be causing the problem.

Uninstall Disk Diet. There is no reason to ever run any "cleaning", "optimizing", "speed-up" or anti-virus apps on your Mac.  This user tip describes what you need to know and do to protect your Mac: Effective defenses against malware and other threats - Apple Community   

Before a full install download and apply the macOS Catalina 10.15.5 Combo Update.  

The report indicstges that you many have installed unknowingly some adware. It appears to be connected to TinkerTool which is a good app. So download and run the free version of Malwarebytes. It was developed by a long time contributor to these forums and a highly respected member of the computer security community. If it indicates it has found the adware and removed it you'll be in good shape.

However, you've installed what many here consider akin to malware: CleanMyMac. Do a Google search for the developer's instructions on how to uninstall. Do not use an app cleaning app that might be offered. Either use the built in uninstaller (if there is one) or the manual method that is described.

You can check to see if you've removed all of the files by downloading and running Find Any File to search for any files with the application's name  and the developer's name in the file name.  For example for CleanMyMac software you'd do the following search: 

1 - Name contains cleanmymac

Any files that are found can be dragged from the search results window to the Desktop or Trash bin in the Dock for deletion.

FAF can search areas that Spotlight can't like invisible folders, system folders and packages.

Good luck. Let us know how it goes.