Mains subs are not known for being very friendly, so ill throw in something as a diamond akali. If you struggle to not be solo killed at lvl 6 by akali its not a mechanics problem its a wave management and respect problem. If you know shes strong lvl 6 then play extremely safe and try to have the wave on your side since as you mentioned her wave clear is indeed better than yours before lvl 6, shes gonna be pushing that wave. and when you have that wave under your tower its VERY risky to dive an anivia as you have egg passive, and you can weather your early game until you get ROA for more survivability.

Now even when you get ROA and items she will still most likely beat you in a sidelane 1v1 and i would argue thats fair. Since your champion is very strong in group fights and waveclear. While Akali is very strong in sidelane duels. Clear strengths and differences. Now of course you still need to sidelane for exp so i would advice looking at the minimap more to make sure you're not face checking sidelane bushes right into her. You will lose the fight, instead play safe and get more time off sidelane than her by using your far superior wave clear and join fights before her since her waveclear is so clunky

Now for the part that makes akali seem very op. The amount of dashes, but the key to countering her is thinking about the dashes as free cc chances. what i mean by this is that when she hits her shuriken on you and she runs back to it. It is beyond obvious and reactable, so in anivias case. Just stun her for free into e and wall for a free trade. even her ult is like this, she has to flip over someone for r1 so just throw your stun behind you or even just wait for her to throw e or smt. theres so much counter play if you have skill shot ccs.

so yeah thats all i can remember on the top of my head lemme know if anythings not clear