How much does the future career of a PhD student matter to the advisor?
Your last sentence makes me think that the question you ask in the title may not be the question you're really interested in. If you feel lost, talk to people. Friends, family, professionals, whichever you feel most comfortable with, but get help.
How much does the future career of a PhD student matter to the advisor? The subsequent careers of the collective PhD graduates influence the attractiveness of the advisor to future PhD students. So it matters, but if the advisor has many successful PhD graduates on their resume, it is a matter of diminishing returns.
Beyond that, a good PhD advisor would feel a moral obligation to ensure their former students land somewhere nice. However, the current Covid situation makes the job market really rather difficult right now, so this is not entirely within the grasp of the advisor. Offering a postdoc is something that the advisor can control, so I can understand why this would seem like a reasonable solution to them.