Hey there,

Actually, Mobile web template is not a native mobile app, so when you browse your website on your mobile phone, it actually need to open on your mobile browser app, then only can see your website.

Mean it will not show the notification pop up on your mobile phone when someone comment/like your status on your website.

In order to push this notification on mobile, you have to consider to use this web push notifications app (https://stackideas.com/apps/item/3355-web-push-notifications)

And keep in mind that web push notification is not supported on IOS mobile devices, you can read more this on OneSignal website https://intercom.help/onesignal/web-push/troubleshooting/web-push-notifications-on-mobile