Do professors actively seek postdoctoral students for projects?
In comparing my experience at several places, and my wife's (in a different field), I think there are two radically different models.

Department has X postdoc (or equivalent, under a different name) positions. Open search to fill based on generic criteria, some degree of importance to &quot;this person will have good research fit here&quot;. Faculty encouragement limited to encouraging promising new researchers in one's network to apply, speaking up that they are a good fit, and then making the new hire feel &quot;welcome&quot;.
As @Buffy wrote, making potential applicants aware, encouraging them to apply is fine, but nothing can be promised, and there is no obligation of the hire to work on any project in particular.

Research lab (Centre, Unit, one professor...) hires postdocs funded by own research funds. While there are generally obligations to evaluate all applicants for the position equitably, a lot more flexibility and expectation for the lab/group to source suitable applicants, and the position criteria may well end up much more targeted to a specific applicant.


By the way, the postdoc transition is -- arguably -- even more of a difficult one that completing a Ph.D., since it is during that period that a researcher becomes truly independent. So the situation that a postdoc has some of the crucial skills for success and not others, and may or may not succeed in developing them, is pretty typical.