If the harmonic balancer did break, you would have incurred much worst damage, e.g. timing cover, radiator, just to name a few. The harmonic balancer is spinnng with your engine (whatever speed that was) and when it breaks, you don't want to be in its way. It looks like your harmonic balancer did not break and your dealer just did you a favour by replacing it and claimed it under the service campaign. You should have thanked the technician for a thorough job.
If the tensioner broke, on the other hand, your belt won't be turning. As a result, it won't drive your power steering pump, won't drive the alternator, hence the battery lite came on. If the tensioner was never replaced, it is very well possible that it is the culprit.

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98 ML320 (gone but not forgotten)