I just checked the settings again. Indeed there is a "Play alarm sound" setting if you scroll down. I guess it was enabled by default in my case (good, since otherwise I might not know that my phone made the call from my backpack).

Slightly off topic, but I did not even notice before the Emergency SOS settings screen has anything below the break. This UI design is just terrible. There is absolutely nothing hinting that you can scroll down:

https://www.tablix.org/~avian/android_13_emergency_sos_setti...

(Looking at the screenshot now, you can just about see that alarm sound setting below the slightly transparent bottom row. That's just about impossible to see on the real phone, plus the row has the usual Android set of buttons on top, obscuring the text even further).