F/U issue for microsoft-edge protocol handler implementation

[simonhong]

1. Update patch file BRAVE_DEFAULT_BROWSER_WORKER_H should be in public section (don't need QA)
2. Move ms_edge_protocol_message_handler.cc to browser/ui/webui/settings (don't need QA)
3. Notify default protocol change to system - W/o notifying, control panel is not refreshed whe when it's already opened (Need QA)

[stephendonner]

Verified PASSED using

Brave	1.35.72 Chromium: 97.0.4692.56 (Official Build) beta (64-bit)
Revision	04da6c66398ca50e603cc236a07dc7dfd3bbc750-refs/branch-heads/4692@{#990}
OS	Windows 10 Version 20H2 (Build 19042.1415)

Used the testplan from brave/brave-core#11445.

Steps:

1. new profile
2. launched the Control Panel for default apps on Windows 10
3. confirmed Microsoft Edge was the default handler for the ms-edge protocol
4. launched Brave
5. confirmed Brave was not the default handler for the ms-edge protocol
6. clicked on the Make default button while the Control Panel was open
7. confirmed Brave dynamically became the MICROSOFT-EDGE protocol handler in the above

example	example