That's a good practice. KeePass 2, KeePassX and KeePassXC, and KeePassDX on Android do this by default as well. It's even better to use the Auto-Type feature of these software, because then the password never gets on the clipboard in the first place.
Some password management programs (I know for KeePassXC) clear the clipboard automatically after several seconds.
Bitwarden does as well, though it seems more like 20-30 seconds.
It doesn't by default (perhaps it depends on which version you first installed) but it is available under File -> Settings -> Options: Clear Clipboard which can e set to never/10s/20s/30s/1m/2m/5m.
This is good to know, but it still doesn't help if there is an application phone app, etc, that monitors the clipboard.