My bad, I misunderstood. For some reason, I thought it was only your wife's phone that was having the issue even though later in your post you said "we". My mistake!
Tests to and from both my brother and sister worked fine on my Android 13 Stable test. One using Android and Google Messages, and the other using iPhone and whatever they use.
None of us on T-Mobile, two of us on AT&T, and the third on Verizon.
Check out the information in the OP of this thread regarding not being able to downgrade from 13 to 12, so you should have the 13 bootloader, and indeed the whole Android 13 OS, on both slots.
Because if there is any problem, it's remotely possible you could brick your phone.
Yes, you can use Android 12 with the Android 13 bootloader. What you cannot and can never do reliably is use two different major versions of Android such as 12 on slot A, and 13 on slot B, because the apps and app data will be shared between them, and at least one, or eventually both will not work correctly because the app data has been "updated" for the newer version of Android.
Thanks, so with OTA even bootloader is flashed to both slots, right?
You're welcome!
No. OTA is an "out of band" update - it's installed to the inactive slot, regardless of whether you use the automatic system OTA, or you sideload the update package.
Not sure this is the case...I don't believe the system does anything to the "old" slot until the next OTA.
It was definitely the case with the Pixel 1 with the first a/b system. It did this so if for example, you're running slot A before the OTA, the OTA updates slot B while you're running slot A, then you reboot, it boots automatically into slot B, then it updates slot A while you're running slot B. This way, if slot B fails for some reason, it'll boot into slot A (which is already updated) with no issues...hopefully.
I mean, I've been wrong before. The Android documents don't mention this but it makes sense to me.
This is the case. The current slot is unaffected in case there is an error in updating the inactive slot or the inactive slot fails to boot. In such cases, the device will revert to the unaffected current slot. Only on the next OTA will the former current slot be updated.
Interesting. I've never heard of that. Always thought the current slot was unaffected until the next OTA update.
Easy way to test this...Someone who updated via OTA can boot into bootloader and use
fastboot set_active other to switch to the other slot. However - I do not recommend doing this on the Android 13 update until the next OTA.
source.android.com
Who knows. I could be remembering wrong. I swear I thought that's what I read about it when I first got my Pixel, and I thought it made sense - once the initially updated Slot B boots successfully, Slot A gets updated to match. After all, I always thought Google wanted both slots to be on the same software as a backup to boot to just in case.
Maybe I'll test it on my unlocked Pixel 1. First I'll flash the full firmware to both slots, then take the OTA and after all success, make comparisons between each slot's Software in Settings. Yeah, I think I'll do that. I don't mind fooling with the old phone.
Yeah this would be a pretty safe idea. I still have my old Pixel 2 that I can try this on as well.Maybe I'll test it on my unlocked Pixel 1. First I'll flash the full firmware to both slots, then take the OTA and after all success, make comparisons between each slot's Software in Settings. Yeah, I think I'll do that. I don't mind fooling with the old phone.
Edit: Triple posting, self! Shame on me!
developer.android.com
I did go through and successfully flashed my PX6 pro to AP1A.240405.002 with KSU using PixelFlasher 6.8.3.0
source.android.com
I am not responsible for anything at all. 
Used a factory image and booted into Android 13. Auto OTA and a sideload of the full OTA will end in the same result as both use
update_engine. I did boot into Android 13 so the ARB counter did get incremented.
