Harry never knew he was a Wizard or could use magic in the first place to suppress magic. He just thought it was "strange"
The Dursleys never liked to acknowledged Harry's magical roots. They just wanted to ignore it. Harry was forbidden to do or mention magic but not beaten about it. Also mainly, he never held back magic. He made the glass disappear, he ended up on his muggle school top when Dudley and his gang were chasing him, he ballooned up Aunt Marge. So he had his own outbursts but they we not exactly parasitical like [spoiler]
An obscurial arises from suppressing magic. Harry was never suppressed, and was in a lesser horrible condition as the [above mentioned person] was.
That is probably the reason Harry never was an obscurial.
One example of someone who might have been an Obscurial was Arianna Dumbledore.
"It destroyed her, what they did: She was never right again,"
Aberforth said. "She wouldn’t use magic, but she couldn’t get rid of
it; it turned inward and drove her mad, it exploded out of her when
she couldn’t control it, and at times she was strange and dangerous.
But mostly she was sweet and scared and harmless."
"[If] the Ministry had known what Ariana had become, she’d have been
locked up in St. Mungo’s for good. They’d have seen her as a serious
threat to the International Statute of Secrecy, unbalanced like she
was, with magic exploding out of her at moments when she couldn’t keep
it in any longer."
I can be almost sure Ariana was an Obscurial.