Shutdown source when not visible option is not working in Studio Mode

Platform

Operating system and version: Windows 10 Pro 64bit
OBS Studio version: 26.1.1 (64bit)

Expected Behavior

Unloads the page when the source is no longer visible (by clicking the eye icon to hide, or not in the active scene).

Current Behavior

The page does not unload in Studio Mode. It will get invisible but once you make it visible again the page still has it's old state.

Steps to Reproduce

1. Add a Browser source that locally changes over time, such as a simple counter. I've made a simple counter here: https://codepen.io/Bob-ber/pen/WNGBRXQ . You can copy paste this in a .html file to test.
2. Select "Shutdown source when not visible" in the properties of the Browser source.
3. In normal mode (not Studio mode), click the eye icon to hide it and then again to make it visible and see if the page has unloaded (refreshed).
4. Now do the same in Studio mode and you will see the page has not unloaded. This is the bug.

Additional information

Reproduce the issue with a Browser source using the linked counter example or a local HTML file, first in normal mode and then in Studio Mode. Trace the Browser source visibility and shutdown behavior in Studio Mode; done means hiding and re-showing the source unloads or refreshes the page as it does in normal mode.