libobs: Deprecate v1 of obs_properties_add_button

[gxalpha]

Description

With v1 of this function, it's unclear where exactly the data pointer comes from or what it is. In fact, this is not determined by libobs, but the consumer. libobs assumes that the caller of obs_property_button_clicked passes an obs_context_data pointer, and then passes the data pointer of that obs_context_data (which, btw, is an internal implementation detail!) as the data pointer to the callback.
In OBS Studio, this is always the private data of the associated object. However, this assumes that there even is such an object (source/encoder/etc), even though properties are meant to be free-standing. This is not just philosophical, because with obs_get_source_properties you can actually get an obs_properties_t that isn't associated with any specific source, at which point you have no idea what the data pointer will be.

For this reason, obs_properties_add_button v1 needs to go. obs_properties_add_button2 can be used as a drop-in replacement. With v2, it's well-defined that the pointer you're passing as priv is the pointer you get back in the callback as data. If you don't care about it, simply pass NULL/nullptr.

Once v1 is removed in the future, obs_property_button_clicked could be replaced with a variant that doesn't take a second argument, as that argument will no longer be used anywhere (although the existing second argument could also just be marked as unused, that would avoid an arguably unneeded breakage).

Contains #12528 to avoid conflicts (I assume that that PR will be merged before this one, but otherwise it's fine for this to be merged first and the other one to be closed).
Depends on obsproject/obs-browser#496.

Motivation and Context

This method is problematic as described above. obs_properties_add_button is basically a drop-in replacement that doesn't have those issues.

How Has This Been Tested?

macOS 26.
Tested that the "Syphon License" button of the syphon source still works.
Tested that the "Open Plug-in Interface" / "Close Plug-in Interface" buttons of the VST filter properties still work.

Screenshot of the docs:

CI will fail until obsproject/obs-browser#496 is merged and the submodule is updated.

Types of changes

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

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.

[gxalpha]

Rebased on master now that the browser update is merged (#12535), CI should work now.