There are many different vendors with slightly different implementations of this, so the reason why you're not receiving a notification on Android may be difficult to track down. However, it usually comes down to some settings preventing notifications altogether. Try these:
Settings > Sounds & Vibration > Do Not Disturb: if this setting is enabled, Push Notifications will not be received. Make sure this is disabled.
Settings > General > Background App Refresh: this setting allows apps to run in the background and must be turned on.
Settings > Apps > Your App > Notifications: make sure the All notifications toggle is enabled.
Settings > Apps > Your App > Permissions: make sure that Notifications is present under Allowed.
Settings > Apps > Your App > App battery usage: make sure your app isn't on Restricted, and optimally on Unrestricted (although Optimized should work too)
Settings > Apps > Chrome > Notifications: ensure that all toggle switches are turned on.
Settings > Apps > Chrome > Power Usage Details: Disable the Manage automatically toggle and set auto-launch, Secondary launch, and Run in background to On.
Settings > Battery > App Launch: Look for the Chrome App, if this is enabled then Push Notifications will not be received. Make sure this is disabled.