We need to find participants easily under the participants menu because there are hundreds of participants in some courses.
For instance, there is such a "find participants" search box for Grade Book list but not for participants list.
I attached the SS1 to this idea.
You know that it is possible to list max 100 participants on the page, the rest is divided into different pages.(Attachment SS2).
Instead of adding search box, maybe you can make it possible to list all participants in one page, then we can use CTRL+F to find specific participant. This can be considered as an alternative and quick solution.