The NFPA Code does not list the requirements for a power supply on a beam detector, as such. However, the beam detector is a fire alarm system smoke detector. Because it is a fire alarm device, it is required to continue operating for as long as the fire alarm system is operating.
To keep the beam detector working, the power supply has to continue to work in adverse conditions.
Just like the main fire alarm control panel is protected, the utility power for the supply has to be protected. The circuit breaker has to be protected from accidental turning off, and the power supply can't be just unpluggable from the wall.
If the utility power fails, the power supply has to continue to keep the beam detector operating for as long as the rest of the fire alarm system operates: 24 hours, 72 hours, or however long. This requires battery calculations using the data sheets from both the beam detector and the power supply.
If there is a problem with the power supply, such as a battery failure or any other fault with the power supply, the fault has to show up a trouble on the fire alarm control panel.
All-Inclusive Equipment Requirements
Look up in the Table of Contents for the NFPA 72 (National Fire Protection Association Code Book #72). Find the article headed by "Equipment and Personnel", specifically "Equipment". The NFPA 72 does say that fire alarm equipment will be listed for the purpose it is used.
In other words, if any equipment anywhere is used in a fire alarm system, it has to be listed for that use in a fire alarm system. The listing is not with the NFPA; the listing is with a third party, nationally known testing facility like UL, ULC, CCC, CE, FM, etc.
Included with that all-inclusive requirement by the NFPA would be the power supply used for the beam detector.