After PR through a PNP, do I have to stay in the nominating province — and for how long?

There is no fixed legal number of months, but this matters: you must have genuinely intended to live in the nominating province when you applied and when you landed. Once you are a permanent resident, the Charter gives you mobility rights to live anywhere in Canada — but moving away immediately after landing can raise misrepresentation concerns, because it suggests your stated intention was not genuine. The honest approach is to settle in the province in good faith; if life circumstances truly change later, that is different.