Aiming the light
Switch the lamp on and the beam follows your cursor across the sky. Sweep it slowly and the symbol stretches as the angle changes, the way a projection does when it hits a surface at a slant. Park it high and it sharpens up.
Below the beam the city is just a black cut-out with lit windows, which is enough. The interesting part is the light.
Bats
Click anywhere above the rooftops and a handful come out. They cross the frame, wrap round to the other side, and flap at their own speeds so the group never quite syncs up. Fill the sky and it stops being atmospheric and starts being a nuisance, which is worth doing at least once.
What search actually does
Comic and film searches have picked up themed treatment on and off for years: artwork in the side panel, a logo with the symbol worked in, small animations tied to a release. Whether the batman easter egg google users remember is running today depends entirely on the calendar.
The same is true of every character tie-in. Grogu google ran for a season, thanos snap for a few weeks. What you can rely on are the rebuilds.