[Problem/Bug]: Unable to allow a custom extension to run in incognito mode

[Recurse-blip]

What happened?

Hello,

We are currently developing software that requires installing a web extension in the WebView2 browser.

However, we are encountering a showstopper where we can't allow the extension to run in private mode.

A binding for this function extensions::util::SetIsIncognitoEnabled would be greatly appreciated: https://github.com/chromium/chromium/blob/933259fd545e669ad640ca5ff5e475387b8fbfdf/chrome/browser/extensions/extension_util.cc#L166C6-L166C27

We have made a demo project to show the issue:
https://github.com/Recurse-blip/webview2extension

We tried manually editing the Preferences file without success see this function
https://github.com/Recurse-blip/webview2extension/blob/main/weview2extension/Form1.cs#L46

Regards,
Bronislav

Importance

Moderate. My app's user experience is affected, but still usable.

Runtime Channel

Stable release (WebView2 Runtime)

Runtime Version

No response

SDK Version

No response

Framework

Winforms

Operating System

Windows 11

OS Version

No response

Repro steps

Use this demo project :
https://github.com/Recurse-blip/webview2extension

Repros in Edge Browser

No, issue does not reproduce in the corresponding Edge version

Regression

No, this never worked

Last working version (if regression)

No response