Between 4:00-5:00 early in the morning, there was a strong power interruption at Kiryat Ata, and my surge protector, where my UPS and my router with its backup battery connected to, entered a 4 min delay.
As a result, my router operated from the battery for 4 mins before returning to the mains power.
Since it in a constant charging even now when I writing this thread?
What this is happening?
Picture of the backup battery in the attachment.

What the manual says about mains interruptions and operation from the battery? Maybe the explanation may be there.
What came to my mind is an intention to prevent damage when the mains is erratic and unstable, as a result of e.g. some i termittent contact somewhere.
So it better disconnects the power at first moment it senses something bad with it and reconnect back when it sees it being decentfor a given amount of time, so when it is more certain the cause was not something that may destroy it.
Even when there is no relay disconnecting anything, just shutting down a typical flyback SMPS makes it to survive nearly 2x hogher overvoltages (so include e.g. Neutral loss) compare to when it is running under load. And that could be easily done by backfeeding the power supply from the battery (the elevated voltage will be sensed by the regulation electronics, which would treat it as too much power delivered, so then shuts the convertor down), even when the SMPS is external to the router and feding by just two conductor cable.

There is no such information about this inside the manual.
The battery is connected to my surge protector to provide additional protection against voltage spike when the power restored and power dips, as well as low and high mains voltage.
The battery voltage is 12V and it somewhat heavy to hold.