According to the U.S. Energy Information Administration, the peak hourly consumption of power in the US occurred on July 15th 2024 with ~745 GigaWatt-hours (GWh).
That number is indeed lower than the total amount of battery capacity in the world.
However, not all Li-ion batteries can discharge all of their energy in a single hour.
The C-rate is the ratio of how fast the battery can be discharged (or charged) relative to its capacity.
A C-Rate of 1.0 means that it can dump all its Amp-hours in a single hour, while 0.5 means it would take 2 hours, etc.
The higher the output current, the more heat you have to dissipate, and the more the cycling stress on the battery.
Smaller, hand held things that people want charging (and discharging) fast tend to be designed to have higher C-Rates. They can also dissipate their heat faster (thanks to a higher surface area to volume ratio) and can be designed to only last a few years max, when compared to a grid scale facility.
Grid scale batteries aren't usually designed for a high C-Rate, as their job is mostly to charge during the day, drain all night, and smooth out the fluctuations from renewables, and last for years to decades.
According to Thunder Said Energy, a target for long term battery storage installations is a C-Rate of 0.25
According to Batteries and Secure Energy Transitions (IEA), the total global supply of batteries was 2,400 GWh and that an average of ~400 GWh were added annually over the last 5 years.
If the total battery storage today is ~3,000 GWh and the average C-Rate is 0.25, then yes, the entire worlds supply of batteries could handle the peak US power consumption in 2024.
If the total supply is ~3,000 GWh and the average C-Rate is closer to 0.33, then the total available power would match the 1,000 TW figure quoted from your original link.