The tomatoes (both cherry and beef) are now sprouting too!
No sign of the physalis or peppers yet (but the chilis took a bit longer to sprout, so I’m not that worried).
Now for a slightly unappetizing photo, sorry guys!
But when I checked the spinach today, it had sprouted – and the “mold” is only on the root of the plants. And now I’m insecure – since it’s only on the roots, it may either be that the seeds are mouldy (thus the spinach would be screwed) or that it’s actually part of the plant.

A quick Google image search brought up several pictures of sprouting spinach, some with slight hairs on the roots, but none as, well, mouldy-looking as this. So probably it is mold.
But I’m keeping this up overnight in hope of hints, then I’ll probably throw the whole pot out.