[ash] Avoid implicit conversion between class GaiaId and std::string

This is a follow-up to https://crrev.com/c/6062397 with the goal to
improve type safety when dealing with obfuscated gaia IDs. The patch
tackles all occurrneces of implicit type conversion between class
GaiaId and std::string under //chromeos.

Change-Id: I9b5ff2131d5afa0d9a250958db7fcd4b862f45e9
Bug: 380416867
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6082373
Commit-Queue: Mikel Astiz <mastiz@chromium.org>
Reviewed-by: Denis Kuznetsov <antrim@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1394247}