My Photo Stream - copy to albums?

On both my MacBook Pro and iPhone 13 mini, I selected all the photos in My Photo Stream and created a new album (called "saved from My Photo Stream" or some such). Will this be enough to keep the images or do I need to copy them into a folder on my computer?

Curiously, I am not able to delete any of the photos in My Photo Stream on iPhone. My Photo Stream is under From My Mac on the iPhone photos app, but it doesn't show on my Mac. I obviously don't know how all this works. 😊 Thanks!