Re-install safari browser to my iPhone

Safari is maintained as a part of iOS. There is no self standing version of Safari

To have a fresh version of Safari, a user has to reinstall the iOS.

https://support.apple.com/ios/update

Safari missing?

Go step by step and test.

1. Search and find

    Search all Home screen pages.

    Do a one finger swipe from the middle of the Lock Screen.

    Enter Safari in search box to show Safari.  

    https://support.apple.com/en-us/HT201285

2. Make sure that Safari is not restricted.

    Settings > Screen Time > Content and Privacy Restrictions

    Enter Passcode if you have set it up

    Allowed apps > Safari

    Turn it on.

    https://support.apple.com/en-us/HT208982

3. Reset Home Screen

    Settings > General > Reset > Reset Home Screen Layout

    https://support.apple.com/guide/iphone/return-iphone-settings-to-their-defaults-iphea1c2fe48/ios