I cannot edit my contact

See the articles https://support.apple.com/guide/iphone/use-other-contact-accounts-iph14a87326/ios

https://support.apple.com/guide/iphone/edit-contacts-iph89a9c71d8/ios

Contacts are neither stored locally on an iPhone nor in SIM. They are synced to an email account that you had Google, iCloud, AOL, Exchange, Outlook, Yahoo or any Other

1. How many Contacts account (email client server) you have?
2. What is your default Contacts Account?
3. Which email account you are using to store Contacts?

• See the GIF below for Contacts and Default Account

• Learn how to add an email account and make it default (Watch the GIF)
• This example is for Gmail but the process remains same for all Google, iCloud, AOL, Exchange, Outlook, Yahoo or any Other

Can you look at your Contacts while in Airplane Mode? If so, your Contacts are stored locally on your phone (Just like mine, and every other iDevice I have ever set up.). When you look at a particular Contact, do you see an Edit link in the top corner that you cannot tap on or do you see no such Edit link?

You may need to perform a forced restart of your phone to shake loose what ever has become stuck.

Force restart iPhone - Apple Support

Good luck.