There is currently a trending issue in the Google Web Search Help forums with complaints around the Google Search App not letting searchers to save images to their devices anymore.
The issue was reported in the Google Web Search Help forums and they wrote "Earlier today my Google app stopped letting me save images to my device. Usually I get a little notification that says "save image" or "share image" but no I only get the notification attached."
Personally, I see the share image button but Aishwarya Tapadar from Google confirmed the issue and said "Thanks for letting us know about this. We've asked our product team to see what's going on here and we'll get back to you shortly. Stay tuned!"
So maybe this is an issue impacting a limited number of searchers?
Forum discussion at Google Web Search Help forums.