The traction battery in our 2007 is long in the tooth. It is still fine for most driving, but it just is not happy running the A/C for long when the car has come to a stop and the motor has turned off. The displayed SOC pretty rapidly descends and soon the motor comes on. To avoid this I have of late been turning the A/C off when the car stops, and then turning it back on before driving off. Even though it has been quite hot lately, with the car set to recirculate it does not heat up all that much at a 45s light, and the SOC does not descend at all with the A/C off. That is certainly easier on the big battery, but is it hard on the A/C, especially the compressor?
A/C isn't going to be an issue. But reconditioning your battery pack needs to be done if you want to maximize it's lifespan because nickel-based batteries loose capacity due to crystallization and need three rounds of deep cycling to break that up and restore capacity every 18 months once they get old. You can learn more here: FAQ (Frequently Asked Questions) | Hybrid Automotive And if you want to build your own battery maintenance gear you can save alot of money. Learn more here: Build Hybrid Battery Maintenance Gear For Under $100 | PriusChat
To answer your question in simple terms: no it won’t. Heck, I do that with my new 2022 Gen4 (however, mine has an electric a/c compressor), but it won’t hurt either one of them.
You'll have to find a better way to brag about your new Prius because Gen2 Prius also "has an electric a/c compressor."