Apple - How do I know if a time machine backup is running?

The canonical way to check status of time machine is to use the utility and check status or for newer os check the current phase only:

 tmutil status
 tmutil currentphase

Now, you have to process the text since it reports exit 0 when running and when it's not running since the status returned - not that there's a correct status.

I would use:

tmutil status | grep "Running = 0;"

That returns 0 if the system is not currently running and 1 if you are backing up. However, back up on High Sierra implies a non-snapshot event. The snapshots literally are to external drives which literally are not APFS. Only the internal SSD gets APFS treatment and the local snapshots are not something that "run" as so much as "just exist" and the "running" if anything is the thinning process - not the backing up process.

The thinning process calls backupd-helper which doesn't have a command line tool to check when done but you can time that running by issuing a blocking call like:

 tmutil thinlocalsnapshots / 1000000000

Above has enough zeros to thin one giga byte - add two zeros to ask for 100 GB back.

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I do want to correct (or at least challenge lightly) the concept of too many snapshots. APFS is a copy on write filesystem and the only examples of this being bad seem highly contrived or non-default configurations. The files that are around are already written to disk. The system just is "lazy" about cleaning them up and doesn't expend any processing time until it knows the a) system is relatively idle b) storage is relatively idle and not yet running low on free space.

Apple is clearly still in flux with how many snapshots to keep mounted, how to set the cleanup thresholds, how many intervals to keep in situations where the external drive is not connected and the local snapshots exist.

You can dig deeper with:

tmutil listlocalsnapshots /
tmutil thinlocalsnapshots / 1
tmutil deletelocalsnapshots YYYY-MM-DD-HHMMSS

Again, I've yet to see a place where I needed to thin or delete snapshots out of the automatic process on local volumes. The delete can be handy when you want to purge a large backup from an external drive. The real lever we used to have was to use Time Machine exclusions to omit the backup of large files that had tiny changes. It remains to be seen how APFS reacts to these files - my guess is you may be able to placethose type of files on a different APFS volume and thin aggressively and periodically or continue to watch the backup exclusions to see if that saves you allocated space without slowing down the copy on write performance and storage benefits.

Undocumented tmutil status

There is an undocumented, and thus subject to change, tmutil status. This call returns the response:

Backup session status:
{
    ClientID = "com.apple.backupd";
    Running = 0;
}

You will need to parse the JSON portion of the response to learn if Time Machine is running.

Look for backupd

On older versions of macOS, if the backupd process is running, then Time Machine is actively backing up.

See the StackOverflow question, Check if program is running with bash shell script? for robust methods of checking for a running process.