Since it never was a problem to install SailfishOS on top of Android13, at least for me, i don’t see any problems using this method if you want to upgrade the pre install Android version.
Also it is a very good solution to migrate your data from a broken phone, which can still be accesed via USB.
Thank you @wetab73 for finding the right partitions, that helped me alot 
Well, before I tried it myself, I actually couldn’t find any explicit confirmation on the forum that using SFOS on top of Android 13 on the 10 III fixes those nasty echo and color banding issues while not causing any noticeable side effects. If such information was available, I would have flashed Android 13 much sooner. Now, after trying it myself, I can recommend it to everyone else, and it would be great if also Jolla could test it and (if they don’t find any problems) possibly officially recommend using it. I guess that it would make a lot of 10 III users happy if they learned that they can get rid of echo and color banding that’s been badly affecting otherwise really superb 10 III experience.
Now, another story is Android 13-based AOSP binaries (SW_binaries_for_Xperia_Android_13_4.19_v2_lena.img) which seems to be the first release since Jolla-recommended Android 11 based SW_binaries_for_Xperia_Android_11_4.19_v9a_lena.img, that doesn’t get stuck during boot (after asking for the security code) and generally seems to work perfectly fine, except than that I could not get mobile data to work with them. But it might be my specific case caused by some other things (especially that I tried it on an old system restored via dd) and after discovering a problem with mobile data I didn’t really give it any further attention and just switched back to A11 binaries, so maybe it should also be further tested, and such combination (underlying Android 13 + Android 13 AOSP binaries) might turn out to provide some further benefits…
Anyway, thank you very much for confirming that @ric9k’s method to unlock fingerprint capture works with the underlying Android 13. I will make a new SFOS dd backup later today and also test it myself.
I also tried the Android13 binary myself, but mobile data and wifi weren’t working. After flashing the Android 11 binaries the phone was stuck at the home screen and i had to reflash.
I think tge problem that i had to reenter my wifi password after restoring the backup is because i flashed it to another phone with a different MAC.
PS: After changing the charging port board on the phone, everything USB related is working again.
During my tests it happened a few times that flashing the oem_a partition with AOSP binaries wasn’t successful. Fastboot was reporting correctly sending the file to the device (and showing that it took some time to do so) but then writing (even though reported as successful) was indicated as having taken 0.0 seconds, and in such cases then there were either problems with booting the device, or previously flashed binaries were still present as if nothing was written.
So now if I see fastboot reporting that writing took 0.0 seconds, I instantly repeat the command to flash it again.
I actually don’t remember if wifi wasn’t working with Android 13 binaries on my 10 III. I’m not even sure if I tested it after I discovered that mobile data wasn’t working (it was shown in settings as “Limited connectivity” or so). I will give those A13 binaries another try today or tomorrow after I make a new backup. I will experiment if maybe reconfiguring my wireless network from scratch, or switching between IPv4 / IPv6 or some other settings in mobile data configuration could make it work.
As for the fingerprints, does @ric9k’s method remove them all, and then they can be normally added anew?
It was very late last night and i didn’t check the flash time from the fastboot command for the binaries. Thanks for the hint.
Yes all fingerprints are removed, with @ric9k commands.
The part about the wifi password was about my previous posting after restoring my first dd backup and not about Android 13 binary images 
Maybe it is a missing kernel module or something else why wifi didn’t work wit the Android13 binaries. If i have some time maybe i’ll look into this again too.
Yes, something in this order, I don’t remember exactly but it is not always easy to recover wifi connections.
However, afaik, wifi data are stored in /home/defaultuser/.local/share/system/privileged/connman/. Each directory there corresponds to a connection and contains a settings file where the access point name and password, SSID, etc can be found.
One can devel-su cat this settings file in terminal to retrieve the passwords.