Is it normal for a Toyota Prius 2007 to lose half of its battery within a ~10 minutes just standing

Yes, you've got several weak and or bad modules in your battery pack. You'll probably trip the CEL soon. You can use the Dr. Prius app to see how bad it is. That's one of the first signs that your traction pack is failing.
Have the mpg been deteriorating over the past year? Burning more gas?
My old Honda hybrid did that for couple of months, before it tripped the CEL. It would drain and recharge to full several times within 5 minutes.

 

Correct. Classic symptoms of a dying hybrid battery. Start saving for a new one. $2,500 or less OEM from a dealership (some people have called the 4 closest dealerships near you and get a quote from each. Lowest I've heard is $1,700 with a core deposit.

 

This does not necessarily mean you have bad modules it could be a uniform reduction in capacity across all modules. An easy way to find out is to do a 3-cycle series of charging and discharging with a final balancing charge. If you do not have the equipment for this or have the inclination or means to acquire the equipment, there is a fellow PriusChatter in WA (about an hour south of Seattle, IIRC) who goes by the handle @PriusCamper who might be available to do that for you for a modest fee. As part of the deal, PriusCamper will be able to check your modules and tell you if any are suspect.