What's the meaning of "These photos will also be deleted from Photo Stream on all your devices"?

I have iCloud Photos, and for a period had iCloud enabled on my iPhone (6, 12.1.2). Then I had disabled iCloud on the phone to free space. Some photos still stayed on the phone and I didn't delete them for a while. Now after some time again my storage is full on the phone and I wanted to delete these photos, which all perfectly synced to Photos on my other Macs, and which I'd assumed are only local copies.

BUT when I tried deleting them I got this message: "These photos will also be deleted from Photo Stream on all your devices". I've checked and Photo Stream is disabled on the phone. It's not clear to me how things work and why I'm getting this message.

Can I safely delete these photos without deleting them from Photos across all devices?

Your photo library is independent of the photo stream. So is opting in to iCloud storage of your photo library.

The only overlap is if you import items from the photo stream into the library. Deleting an item from the photo stream does not delete it from any library so it's safe to delete if you're sure you already have it imported or never want it imported.

• https://support.apple.com/en-us/HT201317

Since everything gets deleted automatically from the stream, you're just accelerating that for the ones you choose to purge early.

I suggest that you have a separate folder on an external drive for all photos as a backup.

I do this and even if I make a mistake between any device and iCloud I still have the originals.

When it warns you that the photos will be removed across all devices then it is best to believe it and make sure.