I do not have an album called My Photo Stream, but if I search for photo stream, 966 photos are listed. How do I make sure this photos are saved?

Have you been using iPhoto or Aperture long ago?

I have been using My Photo Stream with Aperture and iPhoto, until iCloud Photos replaced it. Back then, the photos synced from my iPad have been tagged with the keyword "My Photo Stream". The last photos with this keyword are from 2015, when I migrated my Aperture Library to Photos. Since then, no more recent photos are having this keyword. If you have not been using My Photos Stream during the last 30 days, there will not be any photos to save in the stream, as it is only keeping the photos from the last 30 days in iCloud. An Ubituary of My Photo Stream - Apple Community

On your Mac, any photos that came in through My Photo Stream will have a tag on it that says "Photo Stream". You can view the tags on photos by right-clicking and choosing Get Info. Even after the photo is saved to your Library, the tag remains and that is what you are seeing by searching. You are just searching for the tags on the Photos, it does not mean that the photo will be removed when the My Photo Stream service is shut down.

If you do not have the "My Photo Stream" album in the sidebar, then you will not lose any of those photos.

Actually, the "My Photo Stream" tag may not show up as a keyword in the Info window. Mine don't. The tag isn't in IPTC or Exif metadata. Photos just seems to still have this leftover in its database from way back.

The point is, as Mac Jim ID said, "If you do not have the "My Photo Stream" album in the sidebar, then you will not lose any of those Photos."