I generally recommend that subscribers don't get launch or newsletter emails while they are in the initial welcome series, because they aren't fully onboarded yet.
If you already send the general newsletter, then the easiest thing to do is to tag them when they complete the welcome series. And then send the newsletter to people who have that tag.
Alternatively, you could put them in another email series. That email series could either be like an extended welcome sequence, or it could be an "evergreen newsletter". An evergreen newsletter is like a general newsletter, except that you have the emails in a sequence rather than sending broadcasts. And everyone gets them in order, rather than just getting the latest broadcast email.
For the launch, I think you have 2 options.
1/ Send a broadcast email (or series of emails) to those who have already completed the welcome sequence. And then send another one a few weeks later for those who have since completed the welcome sequence
2/ Set up your launch emails in a sequence (rather than sending broadcast emails). That way, you can automatically send people through it once they complete the welcome series. It does get a bit tricker if you are offering a discount with a deadline, but there are tools that can help with that.
Hope this helps!