What-ho sailors! I just installed Sailfish OS on my Xperia 10 III with all the latest Xperia software and Android 13 updates installed on it. Didn’t revert back to earlier Android versions as was suggested by the official installation instructions.
It was smooth sailing from the start to finish, as I proceeded with the installation following the installation instructions on Windows 11. However, apparently the links to the Sony developer world pages are broken since Sony has closed the developer portal on 8th of May. The xperia x driver and software binaries can be found at https://opendevices.sony.net/. Here’s the direct links to the driver and blob I used: xperia-x-driver.zip and sw_binaries_for_xperia_android_11_4.19_v9a_lena.zip.
After flashing SFOS and booting first time, everything seems to be working so far. This is my first time flashing and using SFOS so proceed with these files at your own risk. 
I installed OP-mobiili, Volvo Cars and Olvid from Aurora Store to quickly test if they work out of the box, but OP complains about incompatible phone and Google Play services (there’s a workaround I haven’t tested yet) and attempt to sign in to Volvo Cars app with my Volvo ID returns with a “permission denied” error, after giving my credentials on redirected Jolla browser.
I will be replacing my Fairphone 6 /e/os with this SFOS Sony Xperia III as my daily driver, if I manage to get these apps working. Had to cancel J2 because of the size of the phone which I can’t use one handed (it’s my main gripe with FP6 too). Xperia III fits my hand far better in this regard. 