A few questions. Why not go straight for your PhD? If you have tons of research experience and decent grades, don't waste time and money on a master's. If you don't know what your career goals are or if a PhD isn't going to help you with those career goals, then I'm not sure getting a PhD for "fun" is a great idea.
If your PI doesn't want you to have hobbies, I wouldn't say that's a good sign, plus, it seems like he's very intentionally dissuading you from joining his group. To do undergraduate work, a masters, and then a PhD in the same lab could signal to people in the future that you're unwilling to get out of your comfort zone. If you can, go to another school for your PhD and at the very least, go to another lab so you can see what else is out there.