Isaac, ‘completed action in the past’ does not distinguish between use of passé composé or imparfait. 

Both passé composé and imparfait refer to 'happenings' in the past (although passé composé is also used for ‘events/happenings/feelings’ true in past and still true currently - see the 2nd link from Hugo Cotton on advanced cases at about 14 minute mark). Imparfait does not refer to something ongoing currently, although it can signify that something was 'ongoing' previously.

The use of imparfait here informs that the speaker sees this as background information,  ‘ongoing’ as she went to work, rather than a specific event in itself. ‘ I was singing…’ rather than ‘ I sang…’

Have a look at the first link from Camille to get a very good, practical description of how and when French speakers use imparfait or passé composé. The use of ‘chantais’ is one of the examples given.

The tense used conveys meaning, in and of itself. The simple little video clips at the end are also useful. 

There are previous responses relevant to this topic that I can’t locate to link to, but hopefully Céline or Cécile will be able to add.

https://www.frenchtoday.com/blog/french-verb-conjugation/passe-composej-versus-imparfait/  

https://www.youtube.com/watch?v=3rpQ5xeFneg