Edge patches Auto update using internal WSUS

My environment doesn't have an Internet connection, we install windows security patches using WSUS.

 

Currently, we are in the process of upgrading all our servers to Windows 2022, since Microsoft edge is part of the image we need to make sure to install the required patches that Microsoft is releasing. with that said, edge patches that are approved in WSUS are showing in "Windows update" on all machines but we need to run our path tool to install the patches that are downloaded from WSUS, which we schedule to do patching monthly once.

Edge is releasing 3-4 updates monthly our patch compliance is dropping. I see edge has an auto-install option (shown in the below screenshot) and we have enabled the option in the registry to check for available updates every 6hrs and install.

But when it is trying to update it fails with the below error, since it trying to reach the internet to get updates.

it looks like "microsoftedgeupdate.exe" trying to download from the Microsoft update site all the time rather than checking in internal WSUS. Is there any way that we can make changes to download edge patches from internal WSUS?