Nothing called "My Photo Stream" exists, just Recents. Is Recents going away??

It doesn't matter to you.

My Photo Stream is shutting down on July 26, 2023. Only the copies of photos stored in the My Photo Stream folder in iCloud will be deleted. Photos in your Photos libraries on your devices are safe. Learn more about this transition and how to keep your photos up to date across all your devices and safely stored in iCloud by reading this support article —> Information about the My Photo Stream shutdown - Apple Support

"My Photo Stream" dates from 2011 and is an old precursor to iCloud Photos which replaced it in 2015*. Many people have never used it or have since transitioned to iCloud Photos. If you don't see a My Photo Stream folder/album in iCloud Photos then you don't use it and don't have to do anything.

1) Go to: Settings

2) Choose Your Name / AppleID

3) Go to iCloud

4) Go to Photos

5) See if you have My Photo Stream. If you do, read the support article about what to do.

You wrote "My Mac iPhoto desktop app says "Library."

Are you still using iPhoto on your Mac? Or is it a typo and you have already moved on to Photos for Mac?

My Photo Stream has been behaving differently in iPhoto from the way it is behaving in the newer Photos. The support document "Information about the My Photo Stream shutdown" does not apply to the older iPhoto - if you still have iPhoto Libraries open them all in turn, to check, if one of them has been syncing with My Photo Stream. In iPhoto we have to enable the automatic download from My Photo Stream. It is not done by default like in Photos for Mac.

It will only matter, if you still have been using My Photo Stream during the last thirty days, as My Photo STraem is caching the photos only for thirty days in iCloud.