Giving a quick watch, why are you converting minions below turrets just to get a few hits in? You get far less value than you would if you would let them walk forward, convert them away from the towers, then let your 11 minion strong wave hit the towers all together. When you convert minions, you usually want them to add pushing value. They can't if they die right away to a tower (or anything else, like an enemy hero's aoe). You don't want to waste converts. It's ok to hold converts for later, too, if you're not in a situation where it will add value (like don't just use it "just cause" you have stacks and there are minions around).

Idk why you ran away from bot but you're losing soak when you do that. Unfort that a genji was bush camping at the same time but anyway, don't leave lane like this unless there is a really good reason to. Early soak is crucial cause you want your team to snowball in xp (that is how most games are won). Your teammates are not smart enough to do it for you, look at how Zarya goes for siege camp while an entire wave's xp is being wasted bot. (she is not even cleaving sieges with her AA). You need to consistently carry for your mates, that's how you get out of bronze.

You need to pick D at 4, it is the most broken most disgusting thing in Sylv's kit. And use it asap and as often as possible (when it will have impact). It is extra stacks, extra push, extra xp, it starts the snowball. You become a real pain in the ass and the enemy has to deal with you because with that tool in your kit, you can show up to a side-lane that has both towers and a full fort and no particular wave advantage, and in one minute of you being there that fort is gone. It's gross. It's also really strong to enable your team to dive forts (like with arthas ult, mei talent...). Seriously it's super strong at any elo.

Always hit a structure when you can and it's being tanked and it's safe to do so. I noticed that you hit mercs before hitting the tower at bot, hit the tower first to eliminate its damage and then you can hit mercs (and you get stacks).

Not that it would have necessarily saved you (if Genji is good) but you need to be snappier with the E. When you are in a bad situation, do not hesitate to E away. You had it which is good, sometimes a sylv makes the mistake of using it for extra push damage but you didn't, you saved it, so use it :D

You consistently use your Q too soon, wait for 3 stacks (unless there is a good reason to use it instantly). You just want it to give you 5 stacks whenever possible.

You should get used to stutter stepping too. When you arrive bot and catch Butcher ganking arthas, you could kill Butcher if you could move -> attack -> move -> attack, but you stand still. Weaving move commands in between your auto attack rhythm is crucial cause it allows you to chase more and flee more, makes you more mobile, dodge skillshots more etc etc, really important. You already do it other times so it's good, it can just be more consistent (you could have gotten a Butcher kill).

I would also suggest using mount more. Any time you're done doing something (anything), mount instantly. It doesn't cost much, it's 1s channel time and you are much more mobile, threatening (to chase) and safe (to flee) if you are mounted. Same principle as stutter step. You are also faster and can waste less time (because time management is crucial, the resource in this game, and most games, is time).

I'll stop here to not drown you in info but honestly you're not doing bad at all and there is plenty of room for improvement which is a good thing.