I would always try to get work as a specialist. Whether I’m a beginner or not. The focus you gain having less responsibility at work will make you more effective than an experienced generalist :)
However, I’m not purist about this. If you’re not sure what you want to specialize in by all means go try a bit of everything. That generally helps. I guarantee you sooner or later you’ll find s niche that you like (that’s key imo! If you’re having fun at work you’re much more productive).
Regarding learning – no dev ever stops (I don’t think) m. Don’t worry about starting a job while learning the project, I’d say it’s quite normal?