Record disk-space metrics in PM's metrics provider

Fixes an issue where the existence of the ProfileManager was checked
after it was used, which caused test failures leading to a revert of the
original CL in https://chromium-review.googlesource.com/c/chromium/src/+/5568632.

Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5392180
Reviewed-by: Francois Pierre Doray <fdoray@chromium.org>
Commit-Queue: Anthony Vallée-Dubois <anthonyvd@chromium.org>
Reviewed-by: Olivier Li <olivierli@chromium.org>
Reviewed-by: Olivier Li Shing Tat-Dupuis <olivierli@google.com>
Cr-Original-Commit-Position: refs/heads/main@{#1306449}
Change-Id: Id5c2cff63548436b61e2ac9d84957d97b8c00a16
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5576534
Cr-Commit-Position: refs/heads/main@{#1307414}