[web] Allow copying the link

Summary:
Call clipboard copy API just like in other places on web. The discussion about operation feedback is still in progress https://www.figma.com/file/a1nkbWgbgjRlrOY9LVurTz?node-id=11400:282507#473816740.

Depends on D8238

Test Plan: Click copy button and check if the link is in the clipboard.

Reviewers: bartek, kamil, inka

Reviewed By: kamil

Subscribers: ashoat

Differential Revision: https://phab.comm.dev/D8239