Fix C++20 issues

[RytoEX]

Description

Fix an include issue for C++20.

Change lambdas from implicitly capturing this to explicitly capturing this as needed.

Motivation and Context

Want to keep OBS Studio ready for C++20 and eventually build with C++20.

How Has This Been Tested?

Tested locally on Windows 11 with:

• Replace implicit lamda captures for C++20 obs-browser#518
• Update lambas for C++20 obs-websocket#1338

See test builds with the original messy branch:

• Building with C++20 (failed due to websocketpp): https://github.com/RytoEX/obs-studio/actions/runs/23929960754
• Building with C++17: https://github.com/RytoEX/obs-studio/actions/runs/23929940788

As written on the obs-websocket PR, we may have to globally switch obs-studio to C++20 while forcing obs-websocket to C++17 until we can resolve the websocketpp issue or replace it.

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:

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