First time you start car it fires up after few seconds,
Once its hot and you stall

or just turn engine off and try to start 5-10 minutes later it cranks very slowly like maybe 1 turn per second. After few seconds of this it will stop and not crank.
Now you mention it , it does sound like a flat battery as in the sound it makes.
But cant be flat as voltage is 12v and ignition lights and music dont cut off, and it will start no problem once it cools down.
Had this happen as well the other day in a car park. Had to get help and get the car pushed into the bay, It then started after i got it in the bay

But turned off the engine and tried to start again and it wouldn't start. Came back 15 minutes later and it started no problem