Harry did write to Uncle Vernon while at school, but he didn't ask his uncle to pick him up, merely notified him: "I'm coming back."
However... he phrased it very politely, trying to avoid offending his somewhat sensitive uncle.
To Harry's surprise, his uncle actually had Hedwig bring back a reply, asking unprecedentedly when he'd be returning.
This left Harry a bit puzzled.
He walked to the platform entrance and pulled out a piece of Muggle currency from his pocket.
Summoning a taxi, he promptly sat down.
The suitcase was already tucked in a small package with a Traceless Stretching Spell, and Hedwig was keeping Pabi company, so he moved effortlessly without needing to lug anything heavy.
Magic, it's very wondrous.
"Today's quite a nice day, isn't it?"
The taxi driver, a middle-aged man, started chatting as soon as Harry got in.
Harry looked out the window; the gloomy weather made it hard to tell if it would rain or not.
"Indeed, it's nice." he said.
Chit-chatting sporadically with the driver during the journey, they faced constant traffic.
By the time Harry reached the entrance of the Broken Cauldron Bar, nearly an hour had passed.
He walked inside the Broken Cauldron Bar, and Old Tom promptly approached him.
"Potter, Mr. Potter, what an honor..." he said.
"Hello, Tom." Harry said, "I need a room."
Old Tom led him upstairs and assigned him a room.
Once he left, Harry took out the pre-prepared Ageing Potion from his pocket.
Soon, a seventeen-year-old Harry appeared in the room.
He changed clothes, kept the remaining Ageing Potion in his pocket, ready to take another sip if needed.
After thinking it over, he pulled out a pair of black gloves and put them on, then left the room.
The Broken Cauldron Bar was always bustling; the sudden appearance of a seventeen-year-old Harry didn't catch anyone's attention.
He approached the wall, tapped twice in sequence, and opened the door leading to Diagon Alley.
His first stop wasn't Diagon Alley; he planned to eat something at a restaurant there to fill his stomach.
He hardly ate anything in the taxi, just some morning food, all of it long digested after bouncing around all day.
After eating and drinking, Harry stretched and rose slowly, leaving the restaurant.
He had to admit, wizarding world French cuisine is truly authentic and delicious.
Upon entering Diagon Alley this time, indeed no one came up to trouble him.
The Dark Wizards weren't fools; after Davima's downfall last time, they've been more cautious.
Especially about wary of men with glasses.
Harry used a Magic Spell to conceal his scar, curious all the while.
Huh, why aren't any Dark Wizards coming to trouble me?
In that case, what about magic wands?
Harry calculated a bit, hmm... one for Ron, Hermione, Neville, Seamus, Cedric... not ruling out new students joining after school starts, Harry felt he should prepare in advance and stock up on a few more magic wands.
But with no Dark Wizards approaching, Harry thought things shouldn't develop this way.
He considered and decided to visit the Bokin Bok Store first.
Upon entering, there was still no one standing behind the counter in the Bok Store.
Harry walked to the counter and rang the bell.
The bell rang out, and soon Mr. Bok appeared behind the counter.
"Oh, it's my esteemed Mr. Sebastian!" Mr. Bok exclaimed oily upon seeing Harry, extending his hands: "Honored, truly honored to see you!"
His politeness had a reason; last time, following "Sebastian - This damn it isn't your business" into the Bok Store, Davima had been transformed into a Flubber Worm, trampled to mush.
Mr. Bok, accustomed to running a shady shop, had honed masterful skills of reading people, immediately locking his attention on "Sebastian."
Of course, Mr. Bok understood why Sebastian had such a foul temper, after all, capable folk like him needed understanding.
Harry gave a brief handshake, withdrew his hand, and said, "Mr. Bok, I need some rare items; last time I knew, you're a capable person, so... I hope you won't disappoint me."
"That's right, that's right." Mr. Bok proudly patted his chicken-like chest: "In this Diagon Alley, let's not discuss anything else, but there's nothing the Bokin Bok Store can't sell if a buyer thinks of it!"
"That's good." Harry casually wiped the Holly Wand with his gloved hands.
Upon seeing the wand, Mr. Bok's eyes went wide.
But he only glanced twice before shifting his gaze away.
"Pray, what do you need?" Mr. Bok asked.
"Phoenix Tears, do you have any?" Harry asked.
"Yes." Mr. Bok nodded quickly, "And cheaper than what's sold outside, only two Golden Galleons and seven Sickles for it."
With that, Mr. Bok took out a test tube to compare.
"I'll take some," Harry said, "How about two ounces of Phoenix Tears."
Mr. Bok calculated briefly and said to Harry, "That'll be nine Galleons and eleven Sickles, affordable."
"Counting money is such a tedious task, isn't it?" Harry took out the money and handed it to Mr. Bok.