This build is specifically catered toward a poke lane. Typically Sivir is played to scale, perma-farming and picking up kills when it's easy. By taking tear and Manamune, as well as using your E, you're able to spam your Q endlessly. You'll eventually have infinite mana, and pressing Q is the main playstyle. It's different from normal Sivir which focuses on maxing her W second and auto-attacking. Racking up the Dark Harvest stacks will help you to scale late game.
One of the main concerns I had about this build was doing damage to tanks (which is what the ADCs are supposed to do). I noticed that taking Serylda's Grudge helps to penetrate armor early, and you can also build LDR for that extra armor pen.
In team fights, you'll need to position yourself to hit as many of the enemy champions with your Q as possible, especially late game where you proc your Hydra. When you have your items late game, you will absolutely OBLITERATE squishes and the backline.
Unfortunately, none of the ADC Mythic items synergize well with Sivir, which is why she's stuck in a hard place in S11. She deals with getting one-shot by anyone on the enemy team as well. This build focuses on centering her damage on her Q- which can help with her positioning far away from the enemy. Instead of her playstyle focusing on her mere 500 attack range, she can play more like a poke-mage.
Hopefully, there will be changes in the future to Sivir or the ADC items, but until that, I believe that this is not only a fun build but one of the most viable ones.

Obligatory flex to show merit: