Revert "Make BrowserContext::GetPath() const"

This reverts commit 8eede4960f0c5494e81ea19a79b9590616126ac6.

Reason for revert: Broke linux-cast-arm64-rel
https://ci.chromium.org/ui/p/chromium/builders/ci/linux-cast-arm64-rel/44763/overview

Bug: 413168662
Original change's description:
> Make BrowserContext::GetPath() const
>
> There is no case where a BrowserContenxt::GetPath() override is not
> a const operation.
>
> Make BrowserContext::GetPath() const to support const-correct APIs
> in downstream code.
>
> Bug: 413168662
> Change-Id: I18f5bcc41df7fed190c7bdaf22e7381b63680dce
> Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6903323
> Owners-Override: Rakina Zata Amni <rakina@chromium.org>
> Commit-Queue: Tom Lukaszewicz <tluk@chromium.org>
> Reviewed-by: Rakina Zata Amni <rakina@chromium.org>
> Cr-Commit-Position: refs/heads/main@{#1508997}

Bug: 413168662
No-Presubmit: true
No-Tree-Checks: true
No-Try: true
Change-Id: I8821f228441adcb6f52349b8a5bd5a5ac877160d
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6903324
Auto-Submit: Tom Lukaszewicz <tluk@chromium.org>
Bot-Commit: Rubber Stamper <rubber-stamper@appspot.gserviceaccount.com>
Owners-Override: Rakina Zata Amni <rakina@chromium.org>
Reviewed-by: Rakina Zata Amni <rakina@chromium.org>
Commit-Queue: Rakina Zata Amni <rakina@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1508999}