[code health] Remove "dangling" label by changing field order.

This CL changes the order of two fields of `BrowserProcessImpl`, so that
the practice suggested in
https://chromium.googlesource.com/chromium/src/+/main/docs/dangling_ptr_guide.md#incorrect-destruction-order
is followed:

    > owning members (`unique_ptr<>`, `scoped_refptr<>`) [should] appear
    > before unowned members (`raw_ptr<>`)".

This changes the order of field destruction and prevents `raw_ptr` from
becoming temporarily dangling. In particular, this CL flips the order of
the following 2 fields:

    ```
    std::unique_ptr<metrics_services_manager::MetricsServicesManager>
        metrics_services_manager_;

    // |metrics_services_manager_| owns this.
    raw_ptr<ChromeMetricsServicesManagerClient>
        metrics_services_manager_client_ = nullptr;
    ```

I noticed this improvement opportunity when working on
https://crbug.com/41485224, so let me also associate that bug with this
CL.

Bug: 41485224
Change-Id: Ie4843657153b0bec33239036b29e050686f0827c
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6483628
Reviewed-by: Ted Choc <tedchoc@chromium.org>
Commit-Queue: Łukasz Anforowicz <lukasza@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1450853}