Yes, got caught with that in the past (i.e. measuring output from a power supply with no load) and thought this time I was doing things right: I added a load on the 5V power rail, since that one was involved in the feedback loop.
But I clearly do not understand power supplies as, after checking and double-checking pretty much all components (thankfully, the design of this SMPS is simple, with not that many components), I decided to plug it into an Amiga A500 and turn it on.
And, what do you know: the clicking stops and power rails all measure as expected.

for the power supply,

for me for getting caught again