frontend: Demangle ScreenshotObj and OBSBasic

[Warchamp7]

Description

This adds a signal to ScreenshotObj so it doesn't have to directly call OBSBasic. Updated after the changes due to the Add Source dialog.

Revised version that supersedes #12186

Motivation and Context

Less friends for OBSBasic and better code.

How Has This Been Tested?

Took screenshots to make sure they still worked.

Types of changes

• Code cleanup (non-breaking change which makes code smaller or more readable)

Checklist:

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

[RytoEX]

This currently has merge conflicts.

[Warchamp7]

This currently has merge conflicts.

Fixed.