Multiple notifications arrive all at once, from multiple apps I'm using an LG Nexus 5X (android 7.0, also did the same on Marshmallow), and over the last few weeks I've noticed that sometimes a load of notifications will come in at once(within seconds), say 3, 5, 10. Some quite old (hours).
eg 5x facebook, 3x email at once. A couple of weeks ago I had 20+ twitter notifications pour in in a couple of seconds.

This doesn't happen all the time, sometimes after I move or wake the phone, so makes me think its suspending notifications based on motion, if that's a thing?! 

It also doesn't appear to be any different on wifi vs 4G, I have no issues with browsing or calling.
Going by your description of not happening when you " move or shake the phone" , it appears to be related to Doze function of Android, which may be the cause

You would need to exclude these apps from the Doze feature. I am not sure how to do that on Nougat but on Marshmallow,   Is there a way to exclude an app from Doze?  should help you exclude those apps ( steps to exclude would probably be similar on Nougat )

Edit: Doze behaviour has been changed in Nougat. Doze is implemented in two stages


  When a device is on battery power, and the screen has been off for a certain time, the device enters Doze and applies the first subset of restrictions: It shuts off app network access, and defers jobs and syncs. If the device is stationary for a certain time after entering Doze, the system applies the rest of the Doze restrictions to PowerManager.WakeLock, AlarmManager alarms, GPS, and Wi-Fi scans. 


My understanding is that this change does not help your problem , without excluding from Doze