[web] Move editAvatarBadge div to EditUserAvatarMenu

Summary:
Currently only the pencil icon is "clickable," we want the whole thing to be "clickable."

Known regression:

The menu is appearing right below the icon rather than below the "badge." Will address this layout issue in subsequent diff.

Depends on D8261

Test Plan: "Whole button" is clickable.

Reviewers: ashoat, ginsu, rohan, inka, michal, kamil

Reviewed By: kamil

Subscribers: tomek

Differential Revision: https://phab.comm.dev/D8263