Open the Google app on your iPhone
Tap your profile picture in the top right
Tap Search history
Tap Delete
Choose Delete today, Delete custom range, or Delete all time
Confirm the deletion
Open Safari or Chrome on your iPhone
Go to google.com
Sign in to your Google account if needed
Tap your profile picture or menu
Tap Search history
Tap Delete
Choose the time range you want
Confirm the deletion
To stop saving future searches, open Search history
Tap Controls
Turn off Web & App Activity