When using iOS Restriction Sets, and the desired behavior is to only "Allow specific apps", adding Web Apps won't allow them on the iOS devices, even though they're on the allowed list.
This is a limitation from Apple, since WebApps / Clips are enabled/disabled on an All-or-nothing fashion.
Apple's documentation states that:
To allow all Web Clips, you need to add the value
com.apple.webapp
Adding the above will allow All Web Apps that are installed on the device to appear. Apple won't allow enabling some Web Apps, it will enable All of them.