Hello Listenlady,
Thanks for those details. Next, let's go to Settings > Siri & Search, and make sure Suggestions while Searching is turned on. Also, make sure in Settings > Siri & Search > Safari all options on that screen are enabled. More info can be found here: Change Siri settings on iPhone
If that doesn't help, let's make sure restrictions are turned off in Settings > Screen Time and check for any content or privacy restrictions that could be preventing you from changing your Safari Suggestions in Settings. More info on the feature can be found here: Use parental controls on your child's iPhone, iPad, and iPod touch
Best regards.