libobs: Fix deadlock on executing tasks

[exeldro]

Description

Fix deadlock on executing tasks

Motivation and Context

Do not keep the task mutex locked while executing a task.
There are multiple tasks in OBS itself and in plugins that use other mutexes and queue tasks.

How Has This Been Tested?

On windows 11 by trying to get deadlocks using an OBS plugin.

Types of changes

• Bug fix (non-breaking change which fixes an issue)

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.