Upgrade to Catalina won't recognize Time Machine on Mac OS Extended (Encrypted)

When using a directly attached external drive for TM, regardless of whether it is formatted in HFS+ or APFS, TM creates a Backups.backupdb set ... which should be accessible with the Finder. Within that set, you should find the computer that was backed up as a "folder" with sub-folders for each backup over time.

If I understood you correctly, you can access these via the Finder, but you are not able to restore them via the TM interface ... correct? If that is the case, then your only option, at this point, is to go ahead and use Finder to extract those files that are critical to you.

Hi there

If the drive isn't detected by migration assistant, try the following:

•If your backup disk is connected to your Mac, make sure the disk is firmly connected, plugged into a power source, and turned on.

•If your backup disk is connected to a network, make sure your Mac and disk are still on the same network, the disk is turned on, and the network isn’t experiencing problems.

•If your backup disk is connected to another computer, make sure the computer isn’t in sleep. If it is, disable the sleep function for future backups.

•If you’re using a Time Capsule as your backup disk, use AirPort Utility to make sure it’s set up properly and connected to your network.

•Click the Finder icon in the Dock to open a Finder window, then look in the Locations section. Your backup disk should be listed. If it’s not, it may be turned off, defective, or currently unavailable on the network.

Completing these steps can help isolate whether the issue is related to the drive or it's connection.

The following page offers additional solutions they may help: If you can't back up or restore your Mac using Time Machine

Cheers!

For better or worse, Time Machine (TM) has evolved with each newer version of macOS.

Now there are three methods available, and relate to the version of macOS running on the source Mac:

1. Source: HFS+ (aka, macOS Extended) to Destination: HFS+ <== pretty much everything prior to macOS High Sierra
2. Source: APFS to Destination: HFS+ <== available from High Sierra to (currently) Monterey
3. Source: APFS to Destination: APFS <== available from Big Sur+; this is where TM is headed for more efficient backups

It's this last method that can pose a problem in that TM backups to an APFS volume, cannot be read by Macs running anything earlier than Big Sur. This is because, TM uses a completely different strategy for making backups to APFS destinations. Sparsebundles gave way to snapshots.

Here's some light reading that you may find enlightening:

• Time Machine to APFS: Evolution - The Eclectic Light Company