[web] Update button label after successful copy

Summary:
Change button label after successful action.

Depends on D8246

Test Plan:
Click copy button and check if the label changes.
Click it repeatedly and check if the label changes back only after 2s. from the last click.
Click it and close modal - nothing should break.

Reviewers: bartek, kamil, inka

Reviewed By: kamil

Subscribers: ashoat

Differential Revision: https://phab.comm.dev/D8294