Can't listen to music via headphones plug (except with headphones)

I have always used my old (2010) MacBook's headphone plug for connecting it to my DAC and listening to music this way.

Now that I've bought a MacBook Pro M3, I tried the same – without success. The headphone plug works with headphones but not with my DAC. The only difference to my former setup is the change of MacBooks.

As soon as I plug in my DAC, the connection is recognized by my MBP – it shows up immediately in the Sound settings –, but no signal arrives at my DAC. I'm clueless. Thanks a lot for a good idea!