eric_
It's time to resolve this old note :-)

Some suggested keys/values would suit well here:
- tourism = attraction,
- office = government,
- government=legislative (see government=legislative -- "legislative" has been used more than "parliament" according to taginfo).

Rather than building = yes, I would suggest building=public (see https://wiki.openstreetmap.org/wiki/Tag:building%3Dpublic)

And indeed, as the building has two distinctive parts (thanks for your contribution), we could use access=public/private for the different parts of this building (multipolygon) and maybe add a description to explain that a bit more.

Remark: this building has been edited since this discussion started. It is now tagged as tourism=attraction, office=government, government=legislative, but building=parliament. Note as well that the surroundings are mapped as well with  name=The Scottish Parliament, the Korean name as well and tourism=attraction. This should probably be removed, except for the Korean name (to add to the main multipolygon)

Let me know what you think and I'll map it accordingly.