Photo Stream vs. Importing Images to Photos App Manually

I'm sorry. I have not used My Photo Stream on Catalina, and I am unable to find a definitive statement from Apple on how it is supposed to work on Catalina.

I hope that somebody who has used this combination (or who is better at the research) will come along and help you with your question.

You should only use My Photo Stream, if you are not using iCloud Photos. Using them together will just complicate things.

You cannot even enable My Photo Stream on Catalina, if iCloud Photos is enabled.

Where are you importing from? From an iPhone or iPad? Or a camera?

My Photo Stream is still supposed to upload all new photos from a device (iPhone, iPad, Mac where it is enabled) to iCloud and will download the new photos on the other synced devices. It will not transfer videos or Live Photos. Don't use My Photo Stream, if you are taking Live Photos and want them alive, because you will have to download the videos and Live Photos separately manually, and the mixed import will be messy.

There are no new features for My Photo Stream on Catalina. My Photo Stream - Apple Support

What version of the Photos application are you asking about? Are you still on "OS X 10.11" as shown above?