I am probably not the one working in an organization where searching for items in Teams sometimes feels like a full time job. There are a lot of folders, an Microsoft is probably working on improving the search experience.
One of the improvements have just been announced ready for shipping: Contextual search, also known as "CTRL+F" for users of Windows. Once the feature becomes available, users will be able to search only in a chat or a specific channel using ctrl+f
This feature should be rolling out soon, and be completed by the end of July. Once again, the roadmap item 64017 doesn't reveal much. But make sure to let your users know when the feature is activated in your tenant. I am sure they will find it useful.