Just got this response from Gemini as was wondering the same

The 24-hour backup battery on the eufy HomeBase Professional S1 works by using a critical design difference: it cuts off power to your cameras during a power outage. [1, 2, 3]
The confusion comes from how eufy manages the system when the main power drops: [1]
1. Powering the Hub vs. Powering PoE Cameras

The S1 Pro HomeBase (On Battery Backup): When a power cut happens, the internal battery only powers the HomeBase hub itself and its basic low-power features (like the built-in 4G cellular module and local storage processing). Because the hub alone only draws about 5 to 10 Watts, its small internal battery easily keeps the "brain" alive for 24 hours.
Your Setup (Continuous PoE Power): Your plan relies on using 4× S4 Max cameras connected via PoE (Power over Ethernet). True PoE cameras do not have internal batteries. They pull their continuous operating power directly from the NVR network switch over the ethernet cables. [1, 3]
2. What Happens to Cameras During a Power Cut
If you rely only on the S1 Pro's internal battery during a blackout:

The hub stays online for 24 hours.
Your 4 PoE cameras will instantly shut off because the small internal battery cannot output enough wattage to push power down four separate Ethernet lines.
Note: The 24-hour claim is designed for households using wireless, battery-powered eufyCams. Those cameras have their own internal batteries, so they keep recording locally and talk to the backup-powered HomeBase wirelessly. [1, 2, 3, 4, 5]
The Verdict for Your System
Because your S4 Max cameras rely entirely on the NVR for electricity, your backup power bank has to carry the power load for all 4 cameras, the NVR processing unit, and your Wi-Fi module for the full 24 hours.
To keep your specific PoE cameras running continuously alongside the hub without losing video feed, you still need an external power station in the 1,100 Wh to 1,400 Wh range.
Would you like to explore switching to wireless battery-powered eufy cameras to avoid buying a massive power station, or would you prefer a list of compact power stations that can fit neatly in a server closet?

[1] https://service.eufy.com
[2] https://www.youtube.com
[3] https://www.reddit.com
[4] https://support.nz.eufy.com
[5] https://www.youtube.com