Summary of User Request
Add client side, immediate "as-you-type" search to the Call Tree panel.
Response and Plan
The current beta version doesn't have any client-side search in the Call Tree, because in practice client-side search turned out to be fairly useless: the client BugJail Application loads the calls lazily / on-demand from the local BugJail Server when you drill deeper, so if you search on client-side, you'll only get results from the parts of the call tree that you've already viewed.
Something may be done for this some day, but the priority is in integrating server side search to Call Tree instead.