[Tab Group Sync] Adopt class GaiaId for improved type safety

The class replaces std::string to avoid bugs when dealing with
obfuscated gaia IDs. The class wraps an std::string and is in most cases
a drop-in replacement.

Temporarily, the class also supports implicit conversion to and from
std::string to allow a gradual adoption, but this functionality will be
removed in subsequent patches.

Change-Id: Ida65280d713b88e13d38ebf1d0bfb4fccf090001
Bug: 380416867
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6063064
Reviewed-by: Rushan Suleymanov <rushans@google.com>
Reviewed-by: Shakti Sahu <shaktisahu@chromium.org>
Commit-Queue: Mikel Astiz <mastiz@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1390494}