mAh stands for mA (milli-ampere) times h (hour) and is the energy of one mA (at a given nominal voltage, so that current times voltage = power) delivered during one hour.
This is correct if the rating is based on a 1 hr discharge rate. While that is possible, AFAIK it's not generally how it's done. As I said in my last post, it's common to specify a 20hr discharge rate, but it can vary by battery type...and I don't have the specs for the specific battery used in the OP's power supply.
If you don't know it, I suggest you read about Peukert's Law.
Peukert's law - Wikipedia
The time interval the mAh rating is based on is called the C-rate.
https://www.dv-power.com/battery-c-rate/
Let's consider a Duracell MN1500. This is their Coppertop AA Alkaline. I believe the common claim is about a 2800mAh rating. The data sheet doesn't give a C-rate but it does have charts that show how the available capacity changes, depending on current draw. [Invalid or Expired Link Removed]
The highest current these show is 1000mA. Note the service hours is about 1hr at 1000mA. So the capacity is only 1000mAh which is way less than 2800mAh.
I believe the 100mA trace bottoms out at about 27 hrs. 27 x 100 = 2700mAh. Still a bit short of the 2800mAh rating, but we are getting close.
Here's a chart for the Energizer Max datasheet
https://data.energizer.com/pdfs/e91.pdf
As you see the capacity decreases as as the current rises. At 25mA you get 3000mAh and the run time is 120hrs. At 500mA it looks like you get about 1800mAh and the run time is 3.6hrs
The Energizer seems to perform slightly better than the Duracell.
Here is a datasheet for a 12V rechargeable battery with a 7Ah rating:
https://www.power-sonic.com/wp-content/uploads/2018/12/PS-1270 technical specifications.pdf
As you see, the 7Ah rating is specified for a period of 20hrs. This table also shows the capacity and current rate for 10hrs, 5hrs, and 1hr.
If it's not clear 7Ah is 7000mAh.