Well, perhaps one interesting moment could be when they are in a dangerous situation in the fanfiction. Harry might use telepathy to quickly communicate a plan to his friends without the enemy noticing. For example, he could send a mental image of a secret passage they can use to escape.
Telepathy likely deepens their relationships. They can understand each other on a more profound level. For instance, they can immediately know if a friend is in distress without having to say a word.
One interesting aspect could be the exploration of new relationships. If Harry Potter is telepathic, it might change how he interacts with his friends. For example, he could communicate secretly with Hermione during class without anyone noticing, adding a new layer of intrigue to their friendship. Another aspect could be in battles. His telepathic ability might allow him to anticipate the moves of his enemies more easily, making for some exciting and different battle scenes.
Maybe his friends betrayed his secrets. In many fanfictions, a friend might accidentally or deliberately let out something Harry had confided in them, like his fears about Voldemort or his feelings for a certain girl. This could shatter his trust.
Maybe his friends in the fanfiction betrayed his trust. For example, they could have broken a promise to him, like not showing up when he really needed them. This would make Harry feel let down.
One great 'Harry is telepathic' fanfiction is 'The Telepathic Bond'. It delves deep into how Harry's newfound telepathic ability changes his relationships at Hogwarts. Another could be 'Harry's Telepathic Awakening' which focuses on his struggle to control this power.
At first, Harry would be in disbelief. He would think it was some sort of joke or misunderstanding. But as the reality sets in, he would become a bit of a loner. He'd still have his sense of right and wrong, so he might continue to fight against the dark forces on his own, all the while hoping that his friends would come to their senses and realize they made a huge mistake in betraying him.
He would probably try to figure out what went wrong. Harry is a curious and determined character. He might start to recall recent events to see if there were any signs of his friends' discontent. He could also try to reach out to them, either directly or through mutual acquaintances, to ask for an explanation.
The Ministry of Magic could also be the main antagonist in this case. If the Ministry is corrupted or under the influence of dark forces, they could manipulate Harry's friends. They might convince his friends that Harry is a danger to the wizarding world order, and his friends, being naive or misinformed, end up betraying him.
One reason could be a misunderstanding. Maybe Harry said or did something that his friends misinterpreted. For example, if he was overheard making a comment that seemed critical of them but was actually taken out of context.