[web] Remove LoadingIndicator from EditUserAvatar

Summary:
In D8285 we introduced a showSpinner prop to the Avatar component. In this diff we remove the LoadingIndicator from EditUserAvatar component and instead pass showSpinner down to Avatar to take advantage of that.

This deduplicates redundant spinner code. Now that we have a "toggleable" spinner in Avatar, components derived from it can use that spinner "for free."

Depends on D8285

Test Plan:
Things continue to look as expected:

Reviewers: ashoat, ginsu, rohan

Reviewed By: rohan

Subscribers: tomek

Differential Revision: https://phab.comm.dev/D8286