[Data Sharing] Add onClick listeners to the share bottom toolbar

Screenshot: https://screenshot.googleplex.com/9hmhSmVpMqyYa46.png

Clicking on the bottom toolbar icon tiles or the bottom toolbar add button will add 1 to the count. This behavior is for prototyping purposes and will be changed later.

Bug: b/324909919
Change-Id: I52efe5e27d80e7effe35bb8c5854c795ea32d077
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5328437
Reviewed-by: Calder Kitagawa <ckitagawa@chromium.org>
Commit-Queue: Hailey Wang <haileywang@google.com>
Reviewed-by: Shakti Sahu <shaktisahu@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1268811}