When measuring the width of a carriage way, what is measures? (on-street parking, painted islands)

I would measure the with from kerb to kerb or end of the paved area if there is no kerb.

(own illustration based on a photo by Thisisbossi, license: CC BY-SA 3.0)

That there is street parking possible can be indicated by a tag with the key parking:lane. That there is a shoulder can be indicated by a tag with the key shoulder. All those are part of a street, are they not? … and users of the data could take those extra tags into account (e.g. when calculating if a over-width vehicle can use this street).

Definitely I would include the parking space if it is subtracted from what is a driving lane if no one parks there ... I am not that sure about the shoulder. If there is a shoulder tag on the highway way I would assume that the width includes the shoulder, as it is mapped as the same object which carries the width. A bit questionable what to think if there is no shoulder tag. And I think, we have no definition of what to include in the width of a "highway".

Some further thoughts: Okay, so, what if a way with a highway tag and a width tag also has a sidewalk tag? Since the width tag is tagged on the way it applies to the whole way – so, if the way includes a sidewalk=both then width needs to include the sidewalk. Mindblowing... More specific width tags may make more sense, I guess. width:carriageway (184 uses) maybe?

We have currently 2037 width:lanes tags, which likely specify the width of the single lanes (see the values at taginfo, too). Maybe specifying this makes more sense – depending on your use case.

Or tag the width of the shoulder in addition to the overall width: width:shoulder (881 uses) or shoulder:width (1906 uses).

I assume, that in the beginning of OSM, when there were no sidewalks, parking lanes, shoulders and stuff tagged onto the same object on which the highway tag was on, the width just meant the width of the carriageway (possibly including such facultative parking like in the photo). While writing this answer I more or less came to the conclusion that, nowadays, a unspecified width tag does not make much sense for ways which have a highway tag, because it is not clear what is meant by it.