rsync has a --info option that can be used to not only output the current progress, but also the transfer rate and elapsed time:
--info=FLAGS fine-grained informational verbosity
The explanation of how to use it comes under the -P option in the man page:
-P The -P option is equivalent to --partial --progress. Its purpose is to
make it much easier to specify these two options for a long transfer that
may be interrupted.
There is also a --info=progress2 option that outputs statistics based on
the whole transfer, rather than individual files. Use this flag
without out‐putting a filename (e.g. avoid -v or specify --info=name0)
if you want to see how the transfer is doing without scrolling the screen
with a lot of names. (You don’t need to specify the --progress
option in order to use --info=progress2.)
So the following:
rsync -r --info=progress2 --info=name0 "$src" "$dst"
Results in the following being output and continuously updated:
18,757,542,664 100% 65.70MB/s 0:04:32 (xfr#1389, to-chk=0/1510)
Note that when the transfer starts the total number of chunks, and therefore the current progress, can change when the recursive option is used as more files are discovered for syncing