In a more positive way, the mask could also strengthen his relationships. If Harry is able to control the mask's power and use it for good, his friends could be even more proud of him. They would see him as not only a hero who defeated Voldemort but also someone who can handle a new and strange magical artifact. However, the journey to get to that point would be full of challenges and misunderstandings. Harry would need to communicate clearly with his friends about his intentions with the mask to avoid unnecessary conflicts.
The mask could potentially strain Harry's relationships. His friends might be worried about him using the mask and getting corrupted. For instance, Hermione could be very cautious and try to persuade Harry to get rid of the mask. This might cause some friction between them as Harry might be more curious about the mask's power.
On the other hand, some characters might be drawn to Harry because of the mask. They could see it as a source of great power and want to be associated with him. But Harry would have to be careful about who he trusts. If he misjudges someone, it could put his real friends in danger. Also, his relationship with the teachers at Hogwarts could change. Some might be more watchful of him, while others might try to take the mask away for safety reasons.