What does this mean, and should I be worried? I feel like I'm being railroaded and pushed out, I don't know if I'm just being paranoid. Also I don't know whether the new team I will be joining will match my skills and interests.
It depends. Did you so far get clues form your manager that they might not want you around for some reason or are you someone who "meets expectations" (to use corporate parlance)? Have they mentioned a reason why you will not be part of the teams that got split? Are your skills better used some place else, like forming a new team with you as a senior?
You know better your context, whatever people on the internet answer can mostly be assumptions.
Is it normal for a manager not to know what team one of his team members is moving to?
Depends on the company. Are you in an outsourcing company or provider, or are you a product company? If the company has clients they are discussing projects with and they still haven't figured out what they want and what kind of a team they need to staff to make it happen, then yes, that can be normal. You are basically "on the bench" until they need you.
Again, you didn't mention the kind of company you work for, so we can't tell precisely.
How do I handle and deal with this news and uncertainty? It is stressful not to know what team I will be moving to, especially when the team might not exist yet.
I don't want this to sound harsh, but for an employer, you are an employee. They will place you where they need you. Now, or when they figure out where they need you. If they figure out they don't need you anymore then that's that. But the same goes for you. If you still like working there then you can stay, if something bothers you then you can leave.
You say the company is restructuring and hiring intensively, are other people in your situation? Try to let emotions aside and think about the big picture and where you might see yourself as part of it.
My manager says that after I help complete the new project with half of the original team [...]
Have they communicated a timeline for how much longer they need you to help or not? They might not know what's coming their way, but they should have a better image about what they need to get done before starting something else. Any communication on this aspect?
What you can do now is to first calm down, then try to look at the whole situation considering all communications about the projects (current and future) not just regarding you, then decide which are the things that you want clarified so that you feel confident that you will still be around in the future.
With that, open a new conversation with you manager and ask them where you fit in in their future plans or what their intention is regarding you. If they can give a straight, honest, convincing answer then you might be good. And if instead you smell bulls#it, then it probably is.
And finally, keep in mind that job security doesn't exist. One day you can be the most dependable person in the company, that everyone wants to work with, and the next you find out that the CEO bankrupted the company, stole all the money and spent it on hookers and cocaine, and now you're all out of a job.
EDIT: Based on the extra details in the comments, it's likely that your manager just knows that you will be leaving his project soon (and his mind is already on that), and then doesn't know what will happen. But instead of saying that, he's trying to give a more acceptable answer of "don't worry, we'll find a team for you". You need a more definitive answer though, so you have to ask again about future plans. You could start the conversation by saying that you will support your current team to the fullest, but that you also want to prepare for your next role, to hit the ground running so to speak, and for that you would need more details. It also doesn't hurt to start "shopping around" and ask other managers or teams if they need someone with your skills.
