But in that case it should have individual battery backup for critical items such as track circuits, colour-light signals and motor worked points. Along with battery backed supplies for lever locks (mechanical boxes) and control circuits, including blocks/bells.
Another method is to use inverters to provide the (typically) 110v 'mains', which can concentrate all the backup batteries in one place.
Many traditional signal boxes may have that. But not all. Those that could be switched out for example, may not have been provided with the ability to operate all functions in the event of a loss of the local DNO mains supply.
For context, many did not have continuous track circuiting, the signals near to the box are mechanical, as are the points near the signal box.
The block always has it's own battery as does any token system.
Low voltage DC track circuits typically have a charger and a single 2V lead acid cell (or they use a primary = non-rechargable cell). Colour light signals typically have a 12V DC head, fed via a 12V charger and a 12V lead acid battery.
Local control circuitry may be fed via a 12V to 50V DC/DC converter. Or it may be a 12V/24V DC/DC converter.
Other arrangements also exist.
And typically, motor worked points may have a battery to reduce the instantaneous load on the power distribution network rather than as specifically back up power.
Yes, another possibility is for a 120V DC to 110V AC inverter. At one time, a modernised signal box (lever frame with all levers removed and all functions replaced by a OCS (one control switch) MES (minimum electrical signalling) panel and new REB (Relocatable Equipment Building) for the interlocking (a route relay interlocking) on the area where I worked had such an inverter. The 19 inch rack included a 110V AC to 120V DC battery charger. There were sixty 2V lead acid cells, each the size of a truck battery. When extra signalling was added, the inverter and it's battery bank were removed and a 650V standby generator was provided.
Before people ask why these type of battery supply arrangements are not used elsewhere, it's because if they were used on large signalling schemes, the cost would far exceed using a UPS and standby generator arrangement both in terms of capital cost and the cost of maintenance.