Did Google remove the "backup while on wifi" option from the Photos app?
OK, so I did some testing and have determined that although the wording on the Photos "Settings" screens has changed, it is still possible to back up your photos solely when the phone is connected to WiFi.

On the Settings-->Back up &amp; sync screen, enabling "Back up &amp; sync" means "WiFi ONLY" by default. Lower on the Settings screen, in the "Cellular data back up" section, enabling "Photos" means that you are allowing photos to back up when on your cellular network. Leaving this switch off will prevent cellular backup of photos, but by virtue of having "Back up &amp; sync" enabled at the top of the screen, your photos will back up via WiFi.

See the screen shot below. I have drawn in red to emphasize the toggle switches mentioned in my answer.