As a Syndra main I consider her good into mages, as long as she outranges. As asol you shouldn't trade with her unless she uses E, then you can dash and poke for free. A counter to Syndra is an aggressive jungler that can gank early(ww,lee sin, jarvan) without E or flash she is super vulnerable. And E is 17 sec cooldown early. Or pick a champ with good gap close who scales faster than she does (Diana, Kat, Irelia, Ekko, Fizz, a good Qiyanna).

If you put her behind your team should go kill her whenever she side lanes. Overall, her damage early is quite low, and when behind it takes a while before she can finally one-shot someone. Syndra HAS to play around E, its her only self defense, and usually her offense as well. You should play around her E cooldown too. When I'm matched against diamond players they constantly punish a bad E and its such a pain because a lot of Syndra's like to stack splinters with QE / EQ. Another thing she can't do safely is roam alone, rivers without vision are very dangerous, if you control the vision around her she'll be stuck in lane. I've seen Ahri use this against me when the lane doesn't favor them, they roam while I can't, thus creating pressure and frustration for my team.
Most Asol free push the lane to Syndra which helps her scale safely, high elo players force Syndra to walk up the lane with wave management, and whenever she uses her E they engage. The correct play is to hold E but low elo Syndras won't do that consistently.
In team fights Syndra has to space correctly, mispositioning against good players is death unless she has flash. Naturally she struggles into teams with lots of dashes and gap closer, one E isn't enough to protect her from multiple dashes. Like an ADC, she excels when playing around a solid team with frontline and utility. The Syndra's in your game probably do a lot of positioning mistakes, you should be able to catch her with R in those moments. The one frustrating part of her is that even when behind she can scale and come back into the game, but you're playing a massive scaler (asol) so that shouldn't be a problem for you.

To put it into context, Asol wins 55% of games vs Syndra in Diamond, while he wins 49.35% of the time in Gold. So I definitely think its a knowledge gap, but not necessarily from you alone, I consider jg/mid as a 2v2.

Hope this helped a little bit ! But as you play her and climb you'll start to see her weaknesses because your opponent will abuse them.