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."

https://en.wikipedia.org/wiki/Scotch_(adjective)

Edit: There is probably absolutely no sensible reason why it is Scots Law but the Scottish Government.

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.

It's both an adjective (equivalent to Scottish or even Scotch sometimes) or a plural noun.

A Scots pine.

It wouldn't be 'a scot pine'

Understable if you're North American, where 'Scottish' is all I really hear. But it is common in the UK, for example 'Scots law' for the legal system in Scotland.

I'm from the UK. Scots as plural is normal. This seems to be singular i.e. The Scottish mayor -> The Scots mayor.

Isn't it singular in e.g. 'Scots law'?

I believe it is still a plural use of Scots i.e. The law of the Scots. "Scots mayor" is in this case is not referring a mayor of Scotland but an individual who is Scottish and happens to be a major. Just seems off. But the writer is German so no worries.

And I'm not trying to be a Scots Inquisition, just interested in language usage :-)

Or a Scotch Inquisition - which is what happens to you if you put Coca Cola in a malt.

Yeah, that's plural.