As well as what it should look like it would be good to know more about how you think it should work. There are many different things that a search in file dialog could do - especially regarding search vs filter. More details would be helpful thanks!

For example, when user have to find some file he needs to search all over the files(sorted lexicographically) manually in a directory, it is a bit inconvenient especially when there is a lot of files. System dialogs usually give ability to search file via Ctrl+F or by clicking at search entry: user types some text into entry, after that new file filter will be applied and the list of files in the directory is refreshed.

Aha thanks, so this is limiting the results in the current directory not searching across the computer?

So we should call this "file filtering"

It is worth noting that the search box in Nautilus (Gnome Files) seems to search in the local directory and recursively down into any sub directories when typing something in to it. I think it is a good way to handle it but in that case I wouldn't call it file filtering.

Yeah, it would be great to search in the local directory and recursively down into sub-directories.