Can I ride on the beach with 32c tires?
While my initial attempt with lightly deflated tires was not a success (I could only bike 100 m before being exhausted) my second attempt went much better.
Based on your helpful answers, comments and suggestions I deflated my rear tire to 1.5 bar, and my front tire to 2 bar and rode at the waterline without much problems at an average speed of 20 km/h.
I was there 1.5 hours after low tide, but there was still plenty of compact sand. Also, it didn't really matter if I was riding on the wet sand at the edge of the water, or a few meters further inland on the drier compact sand, both required approximately the same perceived effort.
Loosened sand (e.g. after dogs have played there) and swathes of shells/seaweed required more effort, so I tried to avoid those.
For context: I use Continental Grand Prix 4 Season 700x32c tires, weigh around 80 kg and am not superfit, but can sustain 25-30 km/h on the road.
Conclusion
Based on my experience: yes, you can ride on the beach with 32c tires if:

You deflate your tires significantly (to 1.5 - 2 bar)
Ride during low tide on the compact sand