So first I went through the replay at 8x speed and only watched the mini map and basically you lost cause you literally didn't do anything until the zerg was building 5 ultralisks. You let him macro and get his 3rd base up unhindered, which is obviously a big no no.
In general, if Protoss lets Zerg get their 3rd base up without much pressure or economic damage Protoss loses 90% of the time. Think of the PvZ match-up as Protoss preventing Zerg from getting a 3rd expansion up.
Lets look at your plan for that game.
You went for a super fast templar archives and built a robo almost at the same time and proceeded to expand around the time storm tech was half way done. Your unit composition was mostly gateway units supported by a few immortals.
If we look at what zerg was doing during all this, we see he went for a 14 hatch and droned up a ton. He took his 3rd base around the time you started researching storm. And your army was tiny, even if you pushed out, zerg could have probably spawned lings in time and would have gotten the expo up regardless.
This super fast templar archives off of 1 base opening is just way too passive. Even if you wanted to, you wouldn't be able to do anything as your stalker and sentry count would be way to low to fight roaches effectively, and I suspect that even if you pushed out with pure zealots and zerg only had lings, he would still be able to build enough lings to to defend.
Rushing for storm just cuts into your unit production too heavily and just takes way too long to finish. Storm itself takes 110 seconds to finish and the templar archives around 50 seconds, that's almost 3 minutes. It also takes a TON of gas to be viable on 1 base.
Archives is 200 gas, plus 200 gas for storm itself, then maybe 300 for a pair of templar. That's 700 gas, could have been 7 sentries or 14 stalkers or a combination of both.
I could go on about how you could have microed the last battle a bit better, but even if you had survived the first wave of lings and infestors without losing anything, you would have lost to the next wave of 60 lings and 5 ultras regardless.
IMO this game was lost because your plan was flawed and you let zerg outmacro you without any pressure.
I'm not saying you should 4-gate every game and not experiment at all, but you should try something more standard first until you get comfortable with it. Knowing one strategy in depth with all it's strengths and weaknesses and being able to execute it perfectly, is much MUCH better then knowing a wide variety of strategies but not being able to do them well.
I think other than that you need to scout a bit better. With your observer you saw double evo chamber, hive, infestors and then an ultralisk cavern and 2 bases. That should have told you immediately to scout for additional expansion, as that's all late game tech/units and is hard to support off of only 2 bases.
I'm guessing all that sounds kinda harsh and disheartening, but keep at it. I haven't watched your other replays, but have you posted a replay of something more standard, like 3-gate robo, or 2 base collossus timing push? Why not just pick a build that's quite common, post a game of you using it (preferably a game where you lose, not much point in analyzing a game you won) and some of us will tell you what you could have done better and you just keep working on it until you're comfortable with it, then move on to the next strategy.
Also next time it would be good to post your own thoughts on the replay as well.
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