The router has its own battery and works as long as the operating voltage of the battery is good.

Yes; the device has a rechargeable battery. If the device is in standby mode, this lasts for approx. 24 hours; otherwise it is also empty after 6-8 hours and must be charged.

Hello !!
Never used the mobile router in USB mode.
Can't help you with that.
Kind regards
Marijo

It is a mobile router,
so it works without a USB cable as long as the battery lasts...

Thanks for the answers, but I'm not sure if the question has been understood correctly. Therefore, I will formulate it in more detail. I have the following scenario:
The router is connected to a Linux PC via USB. The Linux PC sees the router as a local LAN. The power goes out and comes back on after a few seconds. The PC reboots. Will the router also be switched on, or does it have to be switched on again manually?