There actually is a way, and I found it after much searching (as I too was in disbelief that there was such a loophole that made parental controls quite meaningless with respect to blocking search for explicit images, etc.).
What I found is that when we as parents lock everything down via Screentime, that actually disables (vanishes/hides) the “Siri & Search” category in Settings. And that’s the category where you can make the changes to disable images and website thumbnails from appearing in Siri spotlight search. (Yes, it’s absolutely crazy that the ability to lock Siri/Spotlight search down is not in the Screentime settings themselves!)
Anyway, you first need to completely turn OFF Screentime parental controls. THEN you’ll see the “Siri & Search” setting appear again in the iPhone’s Settings. You then go into the “Siri & Search” settings and for EVERY APP listed in there go in and turn off (unclick) all the buttons that are turned on (that are showing the green “on” color).
AFTER you’ve done that, then you need to go back into Screentime, turn Screentime back on, and RESET ALL your Screentime parental control settings and content restrictions like you had them before. Yes, a pain, but hopefully you only have to do it once and your problem is solved.
LAST, check to make sure it fixed the problem. For example, after I did all that on my kid’s iPhone, I pulled down on the screen to show the Siri Spotlight Search bar, and typed in “dog.” And for the first time, it didn’t bring up any images of dogs or thumbnails of websites with dogs. (Alas, kids are not searching for anything as G-rated as dogs, but it should of course not show any results, including when a more explicit search term is used.)
I hope this helps. I found the solution from a parent on another one of these threads. I just did the fix today, and I’m realistic that it’s probably only a temporary fix while kids then find some other loophole. But it’s better than it was before, and I’m actually quite frustrated that Apple didn’t provide a simple toggle in Screentime to disable Siri/Sootlight searches and search results altogether. Here I was as a parent thinking I had Safari and all the apps shut down, and the kids have been able to Siri search for explicit content to their hearts content if they have been so inclined. Alas, such is life in this Brave New World.
Hope this helps, at least.