I'm not sure I quite follow your question, but there are a number of reasons why a parry might not succeed. You might be a little bit early or a little bit late for instance, you might be in the middle of a different animation like an attack or a guard break, or (in rare cases) the attack might be coming from too far around of an angle so that it slips past your guard. Also, if you mash the parry button several times in a row the 'correct' window will reduce significantly, making parrying more difficult.

It is is definitely input-based. The reason you might get hit even if you press block
before a hit is because the timing window is extremely tight. You need to press the button precisely at the moment the enemy's attack is about to connect lots of people finding holding down the block button a little longer then the regular "sekiro" tap much more beneficial.

There is an animation, and the speed is slightly different for different weapons. Not enough to make a huge difference, but it is possible to press in time and be too late with the animation. You also want to hold the button when you parry rather than tapping.

It’s not possible to animation cancel everything into a guard, if that’s what you’re asking. It’s tied to an action state, a pose you strike if you’re not already doing something else, not something you tap to do at any time.

You can usually lop off the endlag of standard attacks, though… In any case, you generally have to press and hold the guard button unless you’re in blockstun which auto-guards in that case. By contrast, there is zero grace period when returning to neutral from an empty guard. The window for a successful perfect guard also decays with each failed attempt within the last couple of seconds.

Never noticed the guard having a windup; if you perceive one then it may be an input delay issue to address on the technical side.

You can see the time it takes to get into the blocking position. Some weapons have a very noticeable windup.

There’s a cosmetic animation associated with guarding that looks different across various weapons, but it has no bearing on the function of guarding itself. I noticed no difference in timing when using the lightest and heaviest weapons in the game. They can both guard the frame the game registers you’ve begun guarding.

But the game doesn't register that you're guarding until you are in the guard position, which is why tapping doesn't work. This is covered here. https://www.youtube.com/watch?v=qkzwPwmoZ2c

It doesn't register that you're guarding unless you're in the guard state. Again, it has nothing to do with the cosmetic 'start of guard to guard loop' transitional animation. It doesn't matter if you're using Wintry Rapier or Frozen Feast; standard guards work the same across all weightclasses and all weapons. In the video you linked, the information at 2:04 is simply factually incorrect. I can see why someone would get the impression because of how tricky heavy weapons can be to use safely, though. It's possible he kept getting caught after swings that left him open.

You can prove this for yourself in under a minute by turning the camera to the side next to the Hotel Krat training dummy and parrying as precisely as possible. Assuming you don't simply tap the guard which will of course leave you open, the only two possibilities are that A) you get hit because your input registered after the dummy socked you and you never entered the guard state (including preceding cosmetic animation) or B) you parry and the weapon snaps into place in front of you even if you started guarding the frame before you were struck.