As an actual Scot it's definitely standard for some things: Scots law, Scots pine. Wikipedia says:
"The use of "Scots" and "Scottish" is not altogether consistent; but in most words and phrases referring to Scotland's people one or the other is normally used: there is a certain tendency for "Scottish" to be used in more formal contexts."
Scots law still seems plural to me i.e. The law of the Scots. Neither example you gave refers to an individual law or pine.
"Scots mayor" in this cases refers to an individual and just seems a little off. Happy to be corrected :) also not a big deal either way as the writer is German.
"The use of "Scots" and "Scottish" is not altogether consistent; but in most words and phrases referring to Scotland's people one or the other is normally used: there is a certain tendency for "Scottish" to be used in more formal contexts."
https://en.wikipedia.org/wiki/Scotch_(adjective)
Edit: There is probably absolutely no sensible reason why it is Scots Law but the Scottish Government.