The Katana's a good bike
Since it's your second bike, it's a good move up, but don't think a sportbike would be too much for you because it's all up to you, not the bike. Besides, sportbikes these days are a huge improvement over bikes, say, 10 years ago. You would have to do something really stupid with the throttle to highside it or flip back. I still get scared sh1tless when I really get on the throttle in 1st-2nd gear, and that's after 4 years of riding it but that's all the fun!
Back in 1990 I was naive enough to buy a Yamaha RZ500 for my first bike. That two-stroke, four cylinder 85 model and I wiped out about a dozen times in the first few months alone
I hear what you're saying, but don't think a 900/1000 would be too much for you. It's not like you have to spend a couple of years in the 250 category, another few years in the 400 category, and so on and so forth. If you're able enough to ride bikes for a couple of years, you're able to tackle bigger bikes because it's all in the mind, as long as you don't bite off more than you can chew and you do sound like you are logical in your approach to riding; it's not like you are speaking like a testosterone driven kid that only wants to impress and brag.
The thing is, do you have a passion for riding or are you doing it for other reasons or out of curiosity, something to try? I tend to procrastinate myself, but not riding because you haven't changed the dead battery doesn't sound like you are all that enthused about riding to begin with.<--well meant