In Catalina, set default for saving files to show extension

This was annoying me too. Today I found a solution. You can now set save with/without extension in every application. As soon as you get the Save screen you can change this and it will be saved for that application

Like StefsterNYC, I had Show all filename extensions checked in Finder > Preferences > Advanced, and therefore could not see the Hide extension option in save windows pictured in sonderpa's answer.

Unchecking Show all filename extensions in Finder > Preferences > Advanced allowed me to see and uncheck the Hide extension option in save windows.

Rechecking Show all filename extensions in Finder > Preferences > Advanced hides extensions (in the filename input field) and the Hide extension option in save windows again. This is a bug and should be reported to Apple (my report's Feedback ID: FB9887776).