If you were using the external hd as your startup disk, then you'll have to reinstall macOS onto that hd.
One way to do that is: if you can boot your MBP normally from the internal drive, then use Carbon Copy Cloner to clone your internal startup drive to the external and restore the bootable capability to that drive.
Another way would be to startup your Mac in Recovery mode (Command-R) and use the Reinstall macOS application to reinstall the OS onto the external drive. In this case you'll first need to ensure that the external hd has been formatted with APFS and a GUID partition scheme for 10.15 Catalina.
How to reinstall macOS - Apple Support
If this is simply a case of being unable to mount the blank, newly erased external drive on the desktop, then use Disk Utility to ensure the drive is formatted with Mac OS Extended (Journaled) with the GUID partition scheme. When that is done, the Mac may recognize it as being useable as a Time Machine backup disk and ask if you'd like to use it as such.
Backup disks for Time Machine - Apple Support