Diederik: I haven't seen an updated kernel yet, but yesterday I noticed apt had an update of firmware-intel-sound, along with a couple other sound-related packages, so I tried booting into 6.0.0-2-amd64 and now both sound and suspend seem to be working.
I wonder if it was something like 6.0.0-2-amd64 changing something in the way it deals with sound cards, but the corresponding firmware update got delayed and didn't get uploaded at the same time. Anyway, I think this is solved now (fingers crossed that it stays solved :-)