Ads after a search

This could be remarketing: the shop reports a product-view event to an ad system, which later picks an ad for the recognised user or browser.

Possible mechanisms: ad pixels and SDKs, cookie identifiers, logged-in accounts and server-side event matching.

To be precise: it doesn't have to mean that the social app read your browsing history. You can't tell the exact mechanism from the ad appearing alone.

Pitfall: one origin's localStorage is not simply readable by any other site. Consent, tracking restrictions and browser settings affect which mechanisms are available.