Hi, Christian!
As it turns out, these two complaints are actually linked to one litttle-known feature that has been part of Cocoa and the Mac for more than 20 years. It’s called the “find pasteboard” and it‘s built-in to native Mac apps by default. It lets you move pasteboard state across your system and around the same application.
To load the find bar with your current selection, you can hold the command key and press E instead of F. To advance to the next findable item with that query, you can press G instead of F.
This also means you can do a find through your document without ever needing to open the Find Bar at all — which is why it does not change its contents when you press the key combination. You may already be looking for something!
As you mentioned, find state commutes between the navigator and editors. It also commutes between applications, so you can start a search in TextEdit or BBEdit and then move to Xcode, or one of many other Cocoa apps on your Mac.
Hopefully this and all the other related power tools we try to give you in the “Find” menu help you fill the gap you feel you’re missing. I know it can be a bit of a transition into this system, and we are always evaluating which paradigms make sense to keep and which may no longer fit with how the Mac is used today, so we appreciate the feedback.