There is definitely no age limit in gymnastics. Btw that's awesome that your doing gymnastics! My dream with gymnastics would be to make a d3 or d2 team in the USA and that's the level and ages they want people to be on their teams.
As for wether you can reach that level...
I think it'll be hard. I think L9 or 10 by that age is unlikely, but I'm always one to say never rule things out. Just try your best, and see where it goes. But remember! Rushing it won't help you reach that level, and especially not with the form D2 or D3 teams want!
However, you seem to be a lot more skilled on bars than on the other apparatusses.
My advise would be to try and keep progressing, tell your coach that you want to go far and really focus on form. A clear hip horizontal with bent arms really just isn't a clear hip horizontal for example. And a cast above horizontal with your feet but with your but low, also isn't a cast horizontal
If you really have the skills you currently have on bars, with strong form and body tension, then I would say keep working on progressions on bars even if you can't compete them. Who knows, maybe when you're older you can look into using your performance on bars for a D3 team? But that's something for later, IF it just happens you progress really solidly.
For now, I really advise to just focus on the journey and to be proud of how you're doing. Don't set your sights too solidly on one dream, there's so much cool stuff you could achieve in your gymnastics. If your path to D3 doesn't work out because it's just too much to catch up, then there's a lot of other cool stuff you can do. And if it does work out that's nice, but don't get too stuck on it I'd say. One season at a time.
As for me, I started gym at age 24

. I wish I could train as many hours as you or with as much help as you get, I mostly have to train myself and ask the coach occasionally for tips or a spot. I train in rec class, but I've done competitions (Recently got gold in womens team finals and in mens al around, you'd have to check that out.)
I regret being too late to do some things in life and in gymnastics, but I have other goals. Current goals include maybe one day competing at an international meet on my level.
And some day a pak salto on bars.