Should I hold back some ideas for after my PhD?
I don't see a point in holding back ideas on purpose, at least not for a longer time.
If you are doing well in research, you will generally have more interesting ideas than you have time to pursue.  And you will keep having new ideas all the time. So there won't be a time when you will have ample of time, but be in desperate need of a great project.
So you should work now on the best ideas you have now: First, people will judge you by your best work and best ideas. If you work on more exciting ideas now, you will be more likely to secure good postdoc positions later. And if you have a fair advisor, they will clearly credit you with those ideas (e.g. in recommendation letters).  So you win by working on your best ideas now.  Second, your best ideas now might be outdated in a few years time, or your interests might shift, or you might have even better and more timely ideas at that time, so there is not much point in saving those ideas.  Third, someone else might have the same idea and publish a result on it in the meantime, making your ideas not new any more.  And finally, even if you don't have the time to work out all ideas fully yourself, it can make sense to share them with colleagues: Maybe they get excited by the ideas and collaborate with you on them, increasing your scientific output.
Finally, what if you will not have good ideas any more in the future? Well, then very likely your chances to secure a permanent position in research are slim, and having kept your old ideas will not save you.