I lost my images

I don't think you fully understood my response.. the only way an iPhone backup would contain your photos is if you were not using iCloud photos..

What does iCloud back up? - Apple Support

But you must have been using iCloud photos if you deleted off one device and they were removed from the other.

Therefore, you would have had to deliberately turn off iCloud photos prior to making your iPhone backup in order for the backup to contain your photos.. and I have my doubts that you did this.

So I'm pretty sure that your photos are gone.

If you think that the backup does contain your photos, then you would need to restore your iPhone from that backup

Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

From what you are describing, you are/were using iCloud to sync your photos.

If you removed them from the Recently Deleted album, you eliminated the only option you really had to recover them.

The only other possibility is if you made an iPhone backup that contains them at a time you weren't using iCloud photos.