OS upgrade to 10.15.6 stuck up

Have you tried shutting down the computer, then restarting it? Press and hold down the Power button until the computer shuts down completely. Wait 30 seconds, then restart the computer. If you cannot restart the computer, normally, then you will have to erase the drive and reinstall macOS. You should be able to do the following:

Erase and Install macOS

If possible, back up your files.

1. Restart the computer. Immediately, at or before the chime, hold down the Command and R keys until the Apple logo and progress bar appear. Wait until the Utility Menu appears.
2. Select Disk Utility from the Utility Menu and click on the Continue button.
3. When Disk Utility loads select the target drive (out-dented entry w/type and size info) from the Device list.
4. Click on the Erase button in Disk Utility's toolbar. A panel will drop down.
5. Set the partition scheme to GUID.
6. Set the Format type to APFS (SSDs only) or Mac OS Extended (Journaled.)
7. Click on the Apply button, then wait for the Done button to activate and click on it.
8. Quit Disk Utility and return to the Utility Menu.
9. Select Install OS X and click on the Continue button.

Reboot the computer. If it's still functioning, then Download and Install macOS Catalina 10.15.6 Combo Update. Always run First Aid on the drive you are updating/upgrading before you update/upgrade. It helps prevent errors from occurring.