Under Sync Preferences, I see "Nightly on Nexus 6P". On Manage Devices page, I see "Firefox Mobile 56. Android 7.1" marked as the current device. On desktop, I don't see neither of the labels in any device list - not in Synced Tabs, not as a target for sending a tab.
Changing the device name changes the problem. I renamed device to "(real)Nightly on Nexus 6P", and I can now see it under Synced Tabs and in a Send Tab list. However, in Manage Accounts that device is still listed as "Firefox Mobile 56. Android 7.1". It seems that we're not keeping our FxA device record up-to-date.
Checking the device list ~5 minutes later, the names now match!