I edit mostly classical music, but in this case the analogy is obvious: the musical is for all practical purposes a modern form of opera , and approach established on MusicBrainz for operas may be easily applied to musicals as well.
In both cases (operas and musicals):
- There is a large umbrella work which consists of smaller parts.
- Usually the umbrella work is performed and recorded as a whole.
- But sometimes smaller parts are performed and recorded separately as stand-alone pieces.
The common approach on MusicBrainz for classical music, including operas:
- Keep track names as printed on CD (include name of the umbrella work only if it is printed on the CD).
- For work names, keep the name of the main work in the title of parts as a prefix. Example from classical music: Acis and Galatea, HWV 49: Act I, no. 7. Aria “Love in her eyes sits playing” (Acis). The main work is “Acis and Galatea”, which consists of Acts (intermediate sub-parts), which consists of Numbers (smallest sub-parts). Applying this approach to the case in question, the work name probably shall be “My Fair Lady: On the Street Where You Live”.
Just for your reference, here is a classical release “The Enjoyment of Opera” with arias from various operas, which is for all purposes similar to your release “Great Songs From The Musicals”: a collection of parts of larger works, recorded as stand-alone pieces.