Remember / prompt with recently used search strings in the search box

[jidanni]

Description

While having to enter the same search string over and over (https://github.com/openstreetmap/iD/issues/10466), I realized that there is no "recently used search" prompts that one would expect in the search box.

Even if one searched for Nerdsome Drugstores a thousand times already today, each time one needs to type or paste the whole thing again into the search box.