In this specific case (Xperia 10 III with Android 13): No (only in this case contrary to Jolla’s statement)
See the FSO thread “Android 13 and SailfishOS on xperia 10 III”. For a summary of aforementioned thread and install directions see my guide “Installing SailfishX on Xperias”.
Note that you might better use the Sony’s software binaries for Android 12 (i.e. SW_binaries_for_Xperia_Android_12_4.19_v2a_lena, explicitly v2a as later versions apparently do not work) for flashing SailfishOS on an Android 12 or 13 base on a Xperia 10 III, also in this very special case contrary to Jolla’s advice. You can easily reflash Sony’s software binaries at any time when SailfishOS is already installed (in contrast to the Android base).
If really (contrary to the experience of others) something does not work, you can still backup the whole SailfishOS installation and downgrade with Emma to Android 11, then upgrade via OTA to the last Android 12 for the Xperia 10 III.
P.S.: As attah correctly pointed out, all this information is already covered in this forum, that is what it is for! You just opened another thread with the same questions, making it harder to find the correct information due to these many duplicate threads. Please do stop this.