[Improvement] Preview of property window will flicker once while switching monitor

Operating System Info

Windows 10

Other OS

No response

OBS Studio Version

27.0.0

OBS Studio Version (Other)

No response

OBS Studio Log URL

https://obsproject.com/logs/XVfCniQ0fMRcnDG-

OBS Studio Crash Log URL

No response

Expected Behavior

After switching new monitor, the preview should be changed as below:

1. firstly, preview may be black because we free the old duplicator;
2. then, preview should be video of new monitor

Current Behavior

After switching new monitor, the preview will be changed as below:

1. firstly, preview will be video of new monitor;
2. then, preview will be black;
3. preview will revert to video of new monitor

This can be reproduced by both "DXGI" and "WGC" modes.

Steps to Reproduce

1. Add monitor source, open its property window;
2. Switch different monitor or check/uncheck "Capture Cursor", look at the preview window.

Anything else we should know?

After debugging, I have confirmed that every time I switched monitor, obs_source_update() will be called twice.
That makes the monitor plugin be reset twice, the flicker is happenned between the two resetting.

1. firstly, preview will be video of new monitor; (first update is done)
2. then, preview will be black; (second update causes free logic)
3. preview will revert to video of new monitor (second update is done)

This issue begins with this commit, please confirm:

Start by tracing the monitor source updates around obs_source_update() for the DXGI and WGC modes, using the provided OBS log and the reproduction steps. Confirm why switching monitors or toggling Capture Cursor triggers two updates, then verify that the preview transitions directly to the new monitor without the intermediate flicker.