NanoPI NEO with router and camera - UPS voltage support on 18650

Good morning,

I wanted to ask for a hint.

I have the following devices
1) Router 12V RUT240
2) NanoPi Neo 12V (step down 12V-->5V)
3) IP camera 12V
4) LIION battery pack with protection (overcharge and discharge) 10Ah
5) LIION 12.6V 3A charger.

I would like the above devices to be backed up from the batteries in the event of a power failure (the NanoPi is to notify of a 230V power failure).
These are connected in parallel to the battery. With a "weak" battery, the NanoPi is supposed to switch off all the devices and finally itself.

1) What phase sensor should I use to connect to the GPIO on the NanoPI and get information about the 230V status? What instead of a 230V relay?
2) While the backup of the devices is implemented and when the battery is completely discharged the devices start up correctly when 230V is applied, I am left with a problem - when I want to shut down a device beforehand, after sending a "shutdown" the Router and NanoPi remain in a "sleep" state. In order for them to start up, the 12V power supply must be disconnected and reconnected. The question is how to implement this? I was thinking of timer relays, but this is not very professional and heavy to implement, as I would also have to use a 'timer' on the 230V side.

Thank you very much for any possible help.