Great stuff as always.
RE: the relationship with the club measure...
"What I don’t know is whether that’s how people interpret it. When relating to the club, who is that? With the owners, players, performances on the pitch or the club as a concept?"
For me, I tend to go with 'all of the above' - a catch-all rating for how people seem to feel overall once all negatives and positives have been balanced up EG people might hate the chairman but love the manager and squad and the social media/"fan engagement", which would ultimately give an overall pretty positive score, despite the one significant negative.
A general barometer for this for me has always been attendances and atmosphere, how people respond to the club on social media, plus some other nebulous, impossible to quantify 'feel' about the place.