It does take some time to get used to a bike that's less stable. That's completely normal. I still remember when I first got my race bike - which is more of a roadrace geometry, not as tight as a criterium bike. Even though I'd ridden tens of thousands of miles on diamond frame bikes, commuting, day riding, and touring loaded and solo all over the region - they'd all been relaxed frames. My race bike felt super twitchy to me, and it wasn't a good feeling at first. But I got used to it. And I grew to love the responsiveness. Give yourself a chance and you will, too.

Now, obviously I don't know how well this particular bike fits you, but if you're talking about all the discomfort you had on your old bike that you're not having on this one, that's a good sign that it fits you well. But, if your steering is extra twitchy because your stem is super short, then that could mean the frame is too big for you. Do you know how long the stem is? (Sometimes the stem dimensions are stamped on it, but that depends on the brand.)

As far as the handlebar width ... having bars of the right width is really important for comfort, but it could go either way as far as your feeling of control.

Are you keeping a nervous death-grip on the bars? That can make your movements jerky, and translate into a twitchy feeling.

Is there a rider skills class in your area that you can take? Those can be super helpful for learning your way around a new bike.

Anyway, good luck and welcome to TE!