What app are you using for contacts?
Are your contacts linked and backed up to your Google account?
There's no menu options while looking at the photos? No three dots or lines on either side at the top, heading (from what you describe yours would probably say "Recent") that you can tap to reveal other options?
Have you viewed the photo you want to use in your Google Photos app and tried "Use as" from there? Mine offers my contact app as one of the options...
If your contacts are Google contacts, linked and backed up by your Google account, you can log in from a browser and edit them there, which will update to your phone when they update.
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