[bedrock] Remove base::SupportsUserData inheritance from Browser

This CL removes the base::SupportsUserData inheritance from Browser now
that all components that were dependent on setting user data on Browser
have been refactored into BrowserWindowFeatures.

Bug: 443772816
Change-Id: Iac286a909dc97559214b1e4c9561b82cdaad31f2
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6927237
Reviewed-by: Tom Lukaszewicz <tluk@chromium.org>
Reviewed-by: Keren Zhu <kerenzhu@chromium.org>
Commit-Queue: Alex Carutasu <alcaruta@microsoft.com>
Cr-Commit-Position: refs/heads/main@{#1513341}