With regards to a group, when do we relate to the group (singular) and when should we relate to the members of the group (plural)

Solution 1:

The definition is consistent with your intuition: It is a group (moreover performing, or meant to perform, as one unit), which is singular. If you want to emphasize the individual musicians' participations then you could word it along the lines as "The members of .."/"They", which is plural.

The intended semantical meaning isn't always polar (discretely singular xor plural) but rather on a continuum, an pragmatic matter of linguistics meets this issue. One potential possibility is to re-word.

A related case can be seen in subject-verb (dis)agreement. Suppose you're inquiring about the musical band / group of musicians:

Who is they?

vs

Who are it?

or explicitly as

Who is this band?

vs

Whom/What members are that that group of musicians composed of?

Another distinction in the pronoun choice is "what" vs "whom": the former implies less relevant sentience or personhood, so "who" might be preferred to agree with humanity. But then that begs the question of Is the 'who' singular or plural? If singular, then that suggests the group being referred as a whole, slightly at odds with opting for 'who(m)' over 'what'. So you must accept that different usages (slight or more divergent) may be suitable, even if the optimal one in a given situation is less common or not totally standard.