It would be nice if Herald transcripts were searchable by object name (like "D123").
Long ago, there was a link from the UI to "Herald Transcripts" for objects, but no one ever clicked it since the use case is very very rare. We could restore this link if we eventually implement some kind of collapsable/accordion UI for action menus, which might make sense (the Project menu is getting huge, too), so we could bury it under "stuff no one ever clicks".
Do you really want application search or just a little search box to look up things by object name?
In the case of the former, I would plan to replace the left nav (a rule-based application search) with a transcript left nave (a transcript-based application search). This feels like it might be a little sloppy navigating around. The alternative would be to "nest" the left navs so we end up with two side by side. That sounds ugly.
So I like the latter better with how I am thinking about this currently.
When you click "Transcripts", I would probably replace the left nav with ApplicationSearch. To get back, you click the application icon in the crumbs. This is a little bit awkward, but I think the most modern/consistent approach available (Harbormaster does this for Build Plans).
The navigation problem is one we have in many applications (Phame, Harbormaster, Drydock, soon Diffusion, possibly Ponder) so I tend to think that adding more instances of it is fine and we can solve them all at once eventually, versus adding a weird custom search instead of ApplicationSearch.