I recall in the past I used to add my Philips hue to both google home and smartthings. In order to prevent the devices from appearing twice I used to use an option in Smarthings to stop Google from seeing it’s lost of Hue devices - but for the life of me I cannot find it now. Has this now disappeared or been superseded by another method.
So if I understand you I should expect to see all the Philips hue lamps appear twice in google home If I link both SmartThings and google home to Philips hue ?