Remove unused deprecated_clipboard_button method

What does this MR do and why?

This change remove the deprecated_clipboard_button which is not used in the code.

It also removes related CSS code that is not used in displaying the clipboard button anymore.

MR acceptance checklist

Please evaluate this MR against the MR acceptance checklist. It helps you analyze changes to reduce risks in quality, performance, reliability, security, and maintainability.

Screenshots or screen recordings

No changes are expected after this clean up.

http://gdk.test:3000/root/Flight/-/branches	http://gdk.test:3000/root/Flight	http://gdk.test:3000/-/profile/keys/1	http://gdk.test:3000/flightjs/Flight/-/settings/repository

How to set up and validate locally

On your local test env, you can try the links I've provided above or some of your own.

Related to #436013 (closed)