The lead is leaded solder is entirely manageable. You should keep track of it all and dispose of it properly. (I.e. not in a landfill.) Wash your hands afterwards. It doesn't vaporize, or at least not in any quantities that you should care about.

As long as you are not directly inhaling in the flux smoke while hovering over the project, it's not that unhealthy. If you are a hobbyist doing an hour of soldering a week, you probably get more smoke particle inhalation making toast. Or pizza. Or frying literally anything.

(If I was soldering for a living, yes I'd want a really good fume extractor on the bench, though.)