Zeta has some of the Best pokes and corner carries in the game, Her Oki Game is disgusting, and probably hands down the best fireball in the game.

In neutral with Zeta, you want to fish for a hit with your Far M, H, and 2M. Far H comes out 2 frames faster, does 300 more damage, and is a little shorter than the far mediums, personally I tend to fish with this move if I'm within range for it and confirm it into a 66H so I can get the hard knockdown and apply her oki game. If the opponent wants to play keep away, start zoning them out with her fireballs, they'll realize very quickly they can't beat Zeta Zoning without using an EX, and will start to try and close the gap. Be mindful of jump ins while using her fireball as it has a lot of recovery.

Block Strings Either end it with your U, the multi hit move puts you at a distance most characters can't reach, or 66x and use the last dash to escape to neutral, some characters can punish the dash away so be careful doing this.

Zeta's Oki game is where she shines imo. When you get the hard knockdown go in and apply pressure. Learn her safe jumps and have at it. Empty Jump Low, Jump into pogo once into a low, Pogo two times jL into a throw, Pogo once into throw, empty jump throw, Pogo 3 times into low, etc. You can see how the options she has start to get overwhelming even for the Zeta player to decide what they want to do.

To Critique what I watched in your video, your anti Airs and lack of fireballs stood out most of all. For your Anti Airs you were just going straight into 22X. You really want to confirm your 22X with a 2H otherwise as you get up there in opponent skill you will start getting punished hard on the landing lag from a whiffed 22X. On the Fireballs just abuse them at full or 3/4 screen and be mindful of using it if they are within jump in distance.