Price history stays on your computer
The history is for the item you asked to watch. When you watch a price, Sidelane saves that product title, URL, and the prices it has seen, in storage on this computer. There is no public catalog of product prices on this site, because Sidelane does not collect what you shop for.
Why there is no page per product
A page that only swaps in a product name, with no prices you actually recorded, would not tell you whether to buy. Sidelane does not publish those pages. The useful history is the one on your computer for the item you are watching.
That history is what a price-drop notice is based on. If the price Sidelane rechecks is lower than the one it saved, you get a notice on this computer.
What a history cannot tell you
It does not include a true total of shipping, tax, and fees. Shipping is unknown unless the store shows it. A code is included only when it was printed on the page.