In Harry Potter and the Order of the Phoenix, Harry is having Occlumency lessons with Snape, to shield his mind from external penetration attempts, after the Arthur Weasley attack.
Before starting each lesson, Snape is extracting some of his own memories and stores them in Dumbledore's Pensieve, to avoid them being seen by Harry, in case the latter one blocks his Legilimency attacks by any means.
Snape was standing with his back to Harry, removing, as usual, certain of his thoughts and placing them carefully in Dumbledore's Pensieve.
Harry Potter and the Order of the Phoenix - Chapter 28 - Snape's Worst Memory
With the knowledge of all the books now, we can deduct that these precious memories most certainly contain the ones he gave to Harry in Chapter 33 - The Prince's Tale of the last book, which reveal his entire backstory.
These memories were crucial in helping him carrying over the task of protecting Harry, undetected. Had Harry seen them 2 years prior, might have changed the course of the entire story, let alone the fact that Voldemort could have easily extracted them from Harry's untrained mind, blowing the cover of Snape.
Yet, when Snape caught Harry inside the Pensieve, he did not show any signs of fear for this. He seemed rather furious that Harry had sneaked inside his own memories, "entertaining" himself:
“So,” said Snape, gripping Harry’s arm so tightly Harry’s hand was starting to feel numb. “So... been enjoying yourself, Potter?”
“N-no...” said Harry, trying to free his arm.
It was scary: Snape’s lips were shaking, his face was white, his teeth were bared.
“Amusing man, your father, wasn’t he?” said Snape, shaking Harry so hard that his glasses slipped down his nose.
“I — didn’t —”
Snape threw Harry from him with all his might. Harry fell hard onto the dungeon floor.
“You will not tell anybody what you saw!” Snape bellowed.
Shouldn't Snape be terrified of the possibility of Harry having seen his backstory and risking blowing the entire plan and his cover to Voldemort?
Someone might argue that Harry was caught while watching this specific memory, but Snape was gone for some time. Who tells him that Harry had not zapped around all the contents of the Pensieve? He neither asked nor tried to confirm (with appropriate or illicit ways) this information.