Closing a VST plugin window with the red cross doesn't signal that it's closed

Operating System Info

Windows 11

Other OS

No response

OBS Studio Version

32.1.2

OBS Studio Version (Other)

No response

OBS Studio Log URL

https://obsproject.com/logs/Hu7PDQBZ8yJtZgPC

OBS Studio Crash Log URL

No response

Expected Behavior

I would expect the "Open Plug-in Interface" button in the "Audio Filters" popup to return to its original state

Current Behavior

After closing the plugin window with its own red X, the button stays on "Close Plug-in Interface" and there is no way to re-open the plugin that was just closed. One has to close and re-open the "Audio Filters" popup for the button to return to normal.

Steps to Reproduce

1. Open a VST plugin that allows the window to be closed (e.g. StereoTool)
2. Close it using its red X

Anything else we should know?

I'm a developer for StereoTool.

Closing the plugin with the "Close Plug-in Interface" works fine, and triggers the same exact code in the VST SDK (and our plugin).
The only thing missing, is for OBS itself to detect that the plugin window is being closed by the OS.

Reproduce the issue with the StereoTool VST plugin from the Audio Filters popup, then trace how OBS handles the plugin window when its red X is used instead of "Close Plug-in Interface." Done means the OS close is detected, the button returns to "Open Plug-in Interface," and the plugin can be reopened without reopening the popup.