So a short report: we have successfully installed Sailfish OS on a Sony Xperia 10 iii that had Android 13 installed before. I did not first flash any Android 11, as it is recommended in the install instructions. The install process was smooth using, as recommended, the SW_binaries_for_Xperia_Android_11_4.19_v9a_lena.zip.
The only thing that does not work is 4G calling / VoLTE – but I think this may be related to the phone provider or something ellse (there is a thread on this here). It needs to be switched off to be able to send SMS.