Tried looking into it now. Took “All Her Fault S01E01” as an example on Peacock.
Indeed it seems like the Peacock mobile app does react to the deeplink while the Peacock TV version is not handling it. This points me to a conclusion that simply the Peacock TV version of their app is just not coded properly to handle these links. There might be nothing more to do here on our side.
For reference this is the direct link from JW: