Move browser-panel ObjC code to Objective-C file; Add more null checks

Description

Moves the Objective-C calls in browser-panel.cpp into an actual Objective-C file, making it more readable. Also adds a !view null check in addition to the existing !*((bool *)view) which might fix a newly reported crash.

Motivation and Context

https://github.com/obsproject/obs-studio/issues/8836 was reported and maybe the first null check fixes it. I have no idea if it actually does since I can't reproduce the crash in the first place.

How Has This Been Tested?

macOS 13.3.1 Made sure that the crash of the original null check added in #374 didn't regress by using twitch integration with and without the call to RemoveNSViewFromSuperview. Whether or not the new crash is fixed I don't know, I guess we'll see when we deploy to production.

Types of changes

Bug fix (non-breaking change which fixes an issue)
Code cleanup (non-breaking change which makes code smaller or more readable)

Checklist:

[x] My code has been run through clang-format.
[x] I have read the contributing document.
[x] My code is not on the master branch.
[x] The code has been tested.
[x] All commit messages are properly formatted and commits squashed where appropriate.
[x] I have included updates to all appropriate documentation.

obsproject / obs-browser