use feature qw(say);

my $rsync_command = 'rsync ... --progress';
open my $RSYNC, '-|', $rsync_command or die "Failed to start rsync: $!";
local $/ = "\r";
while (<$RSYNC>) {
    if (/\A\s/) { # progress lines start with whitespace
        say 'Progress: ', $_;
    }
    else {
        print 'File: ', $_; # file lines have newlines at the end
    }
}
close $RSYNC;