Has it been working alright throughout the rest of the season? I had an HVAC system that was incorrectly wired by the installers, so it actually ran the AC and heat pump at the same time, cancelling each other out. Might not be your situation but you never know!
You can’t “run the heat pump and a/c at the same time” because it’s a single unit. There’s a valve that slides when powered to switch the hot side with the cold side. That’s literally the only difference between a/c and a heat pump.