Extensions: IconVariants: Move `errors` to diagnostics according to plan

The original plan was to use diagnostics instead of updating errors
directly. It was only added initially for faster velocity due to a
reviewer request, which made the original CL merge faster.

Included:
* Simplify the logic to catch all errors after processing everything. No
  longer a need to bail early in the event of an error. This keeps the
  error emittance logic centralized in the diagnostic for loop.
* Remove TODOs. Tests are being added on demand.

Bug: chromium:344639840
Change-Id: I792431d79864ac91bca4dfee85a928dd07d8251c
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6306466
Reviewed-by: David Bertoni <dbertoni@chromium.org>
Commit-Queue: Solomon Kinard <solomonkinard@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1426452}