I'm not aware of any way of doing a search. It might be useful if an array in the watch list could filter to show specific elements, for example all the HTTP elements in the $_SERVER array or all elements that contain a value matching a pattern. I think you would have to write a custom function and use it from the Immediate panel.
However, you can add array elements to the watch list, so you could for example do a watch on
$_SERVER['HTTP_COOKIE'] A shortcut for doing that is to examine the watch of a full array then right-click an element then choose
New watch from here. This does actually satisfy most of my own array watching requirements, but unfortunately doesn't work on object properties as whilst the command is available, I found nothing gets shown, although it does work on array elements within object properties