You should try to use the "sync" command, this is exactly what it solves.
What I end up doing is using a "watch" on some command I can't remember that shows overall dirty pages.
On really new kernels, it might work well to use io_uring to issue linked chains of read -> write -> fdatasync operations for everything the user wants to copy, and base the GUI's progress bar on the completion of those linked IO units. That will probably ensure the kernel has enough work enqueued to issue optimally large and aligned IOs to the underlying devices. (Also, any file management GUI really needs to be doing async IO to begin with, or at least on a separate thread. So adopting io_uring shouldn't be as big an issue as it would be for many other kinds of applications.)