Harry, installed for two weeks at the Leaky Cauldron and told not to go into Muggle London and please don’t go farther than Diagon Alley, spends the two weeks exploring the shops, doing his homework, getting free ice-cream and chats about wizarding history from Florean Fortescue , eavesdropping on other shoppers, and budgeting his savings.
No, seriously, the budgeting is explicit. The text comments that he doesn’t buy several nifty items, including the Firebolt, because “he had five years to go at Hogwarts, and how would it feel to ask the Dursleys for money for spellbooks,”
This is thing, Harry is thirteen and ran away from home, expecting to be expelled, is instead just told “oh god just stay here where it’s safe” and left to his own devices for two weeks. Thirteen year old Harry, unsupervised, quietly enjoys Diagon Alley and budgets himself.