Okay, now I am getting a picture here:Volume up boots the latest TWRP, volume down boots the same "Android Recovery" you mentioned. I'm kinda confused which one is FOTA now...
Sony phones have the recovery-in-boot setup, so you cannot install a custom recovery, because there is no separate recovery partition.
But Custom ROMs can use the Firmware OTA (FOTA) partition, since it's only used by Stock ROMs.
If I understand correctly, LineageOS comes with the "Android Recovery" as a minimal recovery in-boot solution and TWRP in FOTA.
What I didn't know was that FOTA is an actual, writeable partition that allows you to update the TWRP as you would on a regular phone.
The storage access errors my TWRP was giving me stemmed from it being a buggy version that I didn't update, because I thought I could not do that without futzing with the boot image.
After I used TWRP's internal update to bring it to 3.1.1, I still had to manually select the new ROM image (autoupdate doesn't work), but it went through without problems.
So, I guess you also use FOTA Recovery on your phone and never knew