I'm a new postdoc working in a project I really like. I've been there for three months and I'd say I'm doing an acceptable progress. My PI is lovely and we get along quite well, however not long ago I found she's advertising the EXACT SAME project that I'm working on, but this time to get a PhD student. It's the exact same team of supervisors, same techniques, everything, just the position changes. She said the student will be coming around January or February and that she'll make sure they have an independent project, but I just don't understand how this will happen as there aren't enough results to get another project out of this same topic. Is this normal? Should I be worried?
Both that and you being territorial here is normal :)
For a good lab, there is rarely no use for an extra pair of hands. Possibly barring some abstract fields where it's common to work on a problem alone or labs with dozens of people where PI can't supervise them all, too many students is never an issue.
Your goals and capabilities are now different from those of a PhD student and, in turn, different from those of an undergrad. If you both were MSc students it'd be more concerning. Still, the best way to handle that is approaching your PI, ideally knowing which parts of the project are you specifically interested in. An example of PI reasoning might be that for an experiment, you'd need however many samples and that would imply either the new postdoc (you) working over 60 hours a week, scaling the experiment down, stretching it out (which makes the whole project increasingly irrelevant as the time passes) or... well, getting a new student.
I will add a bit to the previous answers.
A project is typically for the funding, aka money. Often there is money left even after hiring one or multiple people, regardless of the status (e.g. postdoc, PhD). It is very common (at least in EU) to hire multiple people under the same project and even shift them here and there depending on the time frame of the funding.
I would say there is nothing to worry about. To make sure you can talk to the PI and ask what would be the responsibilities of the PhD student and if you should help co-mentor and score some additional points there if you want to continue in Academia.