Thanks for the pointer, @smu44.
Since it was still unclear to me which one prevails when they are both set, I did try to set “classic” DNS to 1.1.1.1 (cloudfare) and “Private DNS” to dns.quad9.net (quad9).
https://dnsleaktest.com shows I am connecting via Quad9 (actually shown as WoodyNet as per this comment).
So, the Private DNS setting seems to prevail over the “classic” one.