Searching keys
A recursive scan under the bucket or the open folder — capped, and honest when the cap is what stopped it.

S3 has no search. What it has is a flat listing, so search here is exactly that: a recursive scan with no delimiter, matching your text anywhere in the key.
You choose the scope — the whole bucket, or just the folder you have open — which is the difference between a scan that takes a moment and one that takes a while.
Hits jump either to the object itself or to its containing folder, so a search can be used as navigation: type part of a date, land in the right prefix.
The cap, and saying so
A bucket can hold hundreds of millions of keys. Scanning one unboundedly from a phone, on a mobile connection, would be a bad idea for your battery and your API bill — so the scan is capped at a fixed number of pages.
When the cap is what ended the scan, the summary says “stopped early”. That matters more than it sounds: “no results” and “no results in the part I looked at” are completely different answers, and a tool that conflates them will eventually convince you a file is not there when it is.
Back to S3 & object storage.