Refactor main docks toggle and integration and browser docks

[tytan652]

Description

Dependency of:

• https://github.com/obsproject/obs-studio/pull/7637
• https://github.com/obsproject/obs-studio/pull/7638

Groundwork for other PRs and also avoid creating QActions by using the one included in the dock by modifying its connections making it usable even while the docks are locked.

Motivation and Context

Preparation for PRs that depends on this one.

How Has This Been Tested?

• Test docks toggle with docks locked or not
• Connect to services integration
• Modify custom browser docks

Types of changes

• Tweak (non-breaking change to improve existing functionality)

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.

[tytan652]

Old docks are now added before the separator if it exist.

Edit: I just forgot to add that.