As a Shyvana main, and someone who loves her dearly, could I just offer my opinions?
Please don't change her kit too much. I love all of her abilities.
First off, the animations for Twin Bite and Flame Breath are fantastic. She's got a dragon head on one hand, and the jaw on the other and brings them together for the bit, or puts them together and does a little hadouken so the dragon head is spitting out the fireball. Super cool.
Second, I love how good attack speed is on her. On-hit builds are really fun, and Shyv is the queen of on-hits, mostly due to her Twin Bite, which is a big part of why I wouldn't want it changed, combined with having a couple on hits in her kit.
Burnout is easily her best skill. It's simple, but super effective, and super important to her identity. AOE is a big part of who she is, and so is magic damage. And it's got the most utility as well. On top of that, it's thematically really fun ("I'M A BIG FLAMING BALL OF DRAGON BARRELING AT YOU").
And Flame Breath is simply necessary to have a dragon-feeling kit. Dragons breath fire. You can't just get rid of the fire breath from a dragon kit.
The activation on her ult I love. Figuring out when to use it is one of the biggest decision points in her kit. Should I engage with it? Or save it so I can escape? Use it to clean up? Save it for the knockback so I can interrupt a critical ability like a Katarina ult? Is it worth using in this 1v1 even though it's primarily aoe? Do I need the tankiness? It's one of the reasons she can split-push, a style I enjoy, but I also enjoy that she's in know way locked into split-pushing, she makes an excellent team brawler. And I know it's a slow dash, and easily interruptible, but that is absolutely acceptable for the length of it. Nothing quite like a dragon flying into a skirmish out of the fog of war from a direction you didn't expect.
I also really like that she has strong base stats. I feel it's apropriate. She's a dragon, she should feel powerful.
And one of my absolutely favorite things about her is how varied her build paths are. Good damage items on her: Ravenous, BorK, Triforce, Wit's End, Maw, (almost definitely Titanic Hydra). And none of them are required. You can always adapt your build to what the game needs.
Now, that doesn't mean that I think she should never have any changes and everything about her is perfect. Those are just all the things I like (and I like her a lot). But there are a couple things I wouldn't mind seeing changed, such as:
Her passive. I like the extra tankiness, since I think she needs it, but honestly it's very boring. I it never changed, that'd be fine, but if it did change, I wouldn't be sad to see it go. Especially if it got replaced by something particularly cool.
Her ult other than the dash. The changes to her abilities are likewise fairly boring. I do enjoy them, since it's basically just more aoe, and doubling down on strengths is great. (Love getting both ravenous and sunfire, so much aoe!) But really there's no play there. As long as you're aimed at their team, you're doing it right. Again, one of those things that works and makes sense in her kit, but I'm not really attached to.
Also, I want to say, she's very kiteable. And I'm totally ok with that! She has a lot of strengths, and every champion needs weaknesses. It means you have to be aware of who you're up against, and what abilities they've used yet and pick your battles correctly. She also has a couple tools to work around her weakness, (speed and ult respectively), so she doesn't feel powerless, but by no means do they completely cancel it out.
Anywho, I'm looking at this and thinking wow, this ended up a lot longer than I originally intended. Sorry about that. I just care a lot! If you actually made it all way through the whole thing, thank you so much for reading! I'd love to get in on any conversations about Shyvana (and if they're off in the future, and not happening now, that's cool, that's what you said after all). Just wanted to share my feelings as a player. Thanks again!