I'm sure the information is irrelevant to the question, but I'm running macOS 10.14.6.
Just today I discovered the very interesting tmutil status Terminal command. For instance, while the menu bar icon merely displays "Preparing backup", this command provides actual progress information, similar to this:
Backup session status:
{
BackupPhase = ThinningPreBackup;
ClientID = "com.apple.backupd";
DateOfStateChange = "2019-10-06 15:54:55 +0000";
DestinationID = "XXXXXXXX-XXXX-XXXX-XXXX-XXXXXXXXXXXX";
DestinationMountPoint = "/Volumes/XXX";
NumberOfChangedItems = 2020012;
Percent = 0;
Running = 1;
Stopping = 0;
}
It bears mentioning that this information is continually updated (as fast as I can rerun the command in Terminal), letting me know the backup is progressing, whereas the menu bar icon shows no progress at all during this phase.
And after the actual backup starts, this is printed:
Backup session status:
{
BackupPhase = Copying;
ClientID = "com.apple.backupd";
DateOfStateChange = "2019-10-06 16:14:36 +0000";
DestinationID = "XXXXXXXX-XXXX-XXXX-XXXX-XXXXXXXXXXXX";
DestinationMountPoint = "/Volumes/XXX";
Percent = "2.26301435425844e-05";
Progress = {
"_raw_totalBytes" = 68715697586;
bytes = 1727829;
files = 30385;
totalBytes = 75587267344;
totalFiles = 2093070;
};
Running = 1;
Stopping = 0;
"_raw_Percent" = "2.514460393620488e-05";
}
Clearly this is much more information than the menu bar icon or System Preferences pane provides. On the other hand, it's not too user-friendly: one has to run the command periodically in Terminal, and parse the text output.
Is there a GUI app that presents this information in an easier to read way, which is automatically updated?

tmutiland process it into a form more pleasing to the eye. If you are comfortable using thesedstream editor command in Terminal, this could probably be done in one line of carefully crafted code. I know of no current GUI (or otherwise) app which provides this info. Perhaps this is a good starting point for exploration? – IconDaemon Oct 06 '19 at 17:19