// Nicola took that as support. //
Or course she did. Just as Rishi Sunak does.
The First Minister, like the Prime Minister is not decided by the voters, but by members of the winning party.
After Salmond resigned following the referendum failure, sturgeon was elected leader of the SNP unopposed, and so became First Minister.
At the general election the SNP won 48 seats, and the rest of the parties combined just 11 (including the unseating of the LibDem leader).