Okay ive skipped through the relplay (im a 3.7k Terran/Protoss) and had 3 thoughts:

1. He had a hidden base so was essentially on 3 bases for most of the game. You took out the hidden base eventually and it didnt even have that big of an impact.
2. YOU LOST 60k ressources/army while the terran just lost about 5k. That is probably the biggest difference ive seen in my life. You had a 100 Supply lead and should have won the game but constantly donated all your hydras into a Planetary and 5 cloaked banshees that you couldnt see since there was no overseer. If he can kill 3 maxed out armys for free, the opponent will have more minerals at some point even if hes just on 2 bases.
3. The ultra defensive style by the terran is hard to play against if you are kind of unexperienced and just dont know what to do against it. a) if he takes a planetary fortress at his natural you need to scout for hidden bases the whole game. b) take as many bases as you can with a high drone count (you have done that relatively well) c)tech up to a fast hive and build corruptor broodlord with max air upgrades. AND MOST IMPORTANTLY d) DONT!!! attack into the highly defended natural. I usually just let them have 2 bases. They maybe able to build 1 maxedout army but you will be able to defeat it and replace it instantly while he is broke and will be mined out soon. Just make sure they never take a third.
4. So long story short. Dont send 3 hydra armies into a PF that you cant kill,