#Harry didn’t emotionally understand the death yet.

The J.K. Rowling Pottermore writing on Thestrals explains more clearly what is necessary to be able to see Thestrals. Though it’s been somewhat covered in interviews with J.K. Rowling, this writing goes into a little bit more detail and states why Harry couldn’t see them returning home after Cedric’s death - he hadn’t emotionally understood death yet.

Being able to see Thestrals is a sign that the beholder has witnessed death, and gained an emotional understanding of what death means. It is unsurprising that it took a long time for their significance to be properly understood, because the precise moment when such knowledge dawns varies greatly from person to person. Harry Potter was unable to see Thestrals for years after his mother was killed in front of him, because he was barely out of babyhood when the murder happened, and he had been unable to comprehend his own loss. Even after the death of Cedric Diggory, weeks elapsed before the full import of death’s finality was borne upon him. Only at this point did the Thestrals that pull the carriages from Hogsmeade Station to Hogwarts castle become visible to him. On the other hand, Luna Lovegood, who lost her own mother when she was young, saw Thestrals very soon afterwards because she is intuitive, spiritual and unafraid of the afterlife.
_{^{Thestrals (Pottermore)}}

This writing also explains there’s no set time frame for people to begin seeing Thestrals - it varies heavily between individuals. Harry hadn’t processed Cedric’s death by the time he was leaving Hogwarts at the end of his fourth year, but by the time he returns to Hogwarts for his fifth year, he understood the “import” of it and was able to see the Thestrals. In contrast, Luna saw Thestrals much quicker after her mother died.

While it’s not outright stated, it seems to be implied that the death witnessed would have to be one that would need to be emotionally processed, meaning one that the person would have to feel some amount of grief for.

Harry didn’t emotionally understand the death yet.

The J.K. Rowling Pottermore writing on Thestrals explains more clearly what is necessary to be able to see Thestrals. Though it’s been somewhat covered in interviews with J.K. Rowling, this writing goes into a little bit more detail and states why Harry couldn’t see them returning home after Cedric’s death - he hadn’t emotionally understood death yet.

Being able to see Thestrals is a sign that the beholder has witnessed death, and gained an emotional understanding of what death means. It is unsurprising that it took a long time for their significance to be properly understood, because the precise moment when such knowledge dawns varies greatly from person to person. Harry Potter was unable to see Thestrals for years after his mother was killed in front of him, because he was barely out of babyhood when the murder happened, and he had been unable to comprehend his own loss. Even after the death of Cedric Diggory, weeks elapsed before the full import of death’s finality was borne upon him. Only at this point did the Thestrals that pull the carriages from Hogsmeade Station to Hogwarts castle become visible to him. On the other hand, Luna Lovegood, who lost her own mother when she was young, saw Thestrals very soon afterwards because she is intuitive, spiritual and unafraid of the afterlife.
_{^{Thestrals (Pottermore)}}

This writing also explains there’s no set time frame for people to begin seeing Thestrals - it varies heavily between individuals. Harry hadn’t processed Cedric’s death by the time he was leaving Hogwarts at the end of his fourth year, but by the time he returns to Hogwarts for his fifth year, he understood the “import” of it and was able to see the Thestrals. In contrast, Luna saw Thestrals much quicker after her mother died.

While it’s not outright stated, it seems to be implied that the death witnessed would have to be one that would need to be emotionally processed, meaning one that the person would have to feel some amount of grief for.