iPhone homepage no longer displays the Settings icon

iOS 15 how do I reset Home Screen layout … - Apple Community

though if it was me then I would place my finger on the screen not touching any icons

move it down a bit reveling the search field in that then I would type settings then it should show the settings icon and to the right of it a text telling the folder you placed the settings in by accident

Use App Library to search Settings icon, see this Apple article:

Organize the Home Screen and App Library on your iPhone

Organize the Home Screen and App Library on your iPhone - Apple Support           

If you have find the app, tap & hold on the app, then drag to the Home screen & drop it.