Pass profile as arg to `PostProfileInit`

This is a no-op refactor to change the method's signature and remove the
`ChromeBrowserMainParts::profile()` getter. It is done in preparation
for changes to call `PostProfileInit` after each profile's creation.

Bug: 1150326
Change-Id: Ia2fa8a5510c39cb2757fe2cb5614e984bbb41b84
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/3289419


Reviewed-by: David Roger <droger@chromium.org>
Reviewed-by: Alex Ilin <alexilin@chromium.org>
Commit-Queue: Nicolas Dossou-Gbété <dgn@chromium.org>
Cr-Commit-Position: refs/heads/main@{#958202}