Also, the data you wrote to a file before the rename may not have been flushed completely to cold storage. Rename doesn't change here anything. The data may still be served from the disk controller's cache.

The rename trick is mostly useful for "committing" long operations, which even on the high level are not atomic. But it has nothing to do with flushing.

Also, renaming a file is a filesystem-level operation. From the POV of a disk, it looks the same as any other write. So if you can't make sure that normal writes are flushed, you can't make sure that renames are flushed.

Another note: rename(2) used not to be even atomic wrt power loss on ext4 (which was later fixed), so it's not guaranteed. POSIX itself only guarantees atomicity wrt other filesystem operations. Atomicity against power loss is a distinct checkbox. You need to check your specific filesystem.