Q: Face recognition process does not start

The library the photos app is running with is on an external hard drive.

Has this library been enabled as your system photo library in the Photos > Preferences > General?

What kind of external drive are you using? Is it locally mounted and is the file system MAcOS Extended (Journaled)?

How long have you given it? Try leaving the computer powered and on over night with no programs running and see what occurs

LN

Do other applications see your Photos Library in the Media Browser?  Mail, Preview for example?  If not, the imageanalysisd process may not be able to find the library.

Is your library an iCloud Photo Library, where the photos need downloading?

If the Media browser does not show your Photos Library, try to repair it.

https://help.apple.com/photos/mac/1.2/index.html#/pht6be18f93

My library did not report any progress of the scan for more than four days. But then it suddenly finished.

if you have not done so, restart the Mac to kick of the scanning again;

Keep Photos running, but do not use it; make sure that the Mac will not fall asleep by changing the System Preferences > Energy Saver; the external drive must not be put to sleep while the faces scan is running.