By filtering for MMC1 from your file ("grep mmc1 Putty*.txt") :
You Xperia detects the slot holder manipulation "slot status change detected", but then absolutely NOTHING happens.

This is obvious if you compare with my report.

At this point it is clear, the 128GB card is not seen at all by the Xperia.

Good luck with your work ! (And who knows, maybe by the time you're free again, some solution would have popped-up, or an update would have fixed everything).

I was more thinking of some on/off mechanical problem, like this card being a few mu-meters thinner or thicker beyond the official specs and thus the slot holder not always making perfect contact.

But the fact that systematically on several phone, Android (which I imagine up-to-date, as required by the Sailfish X upgrade) manage to see card, and then Sailfish X after the update suddenly is unable to see it, makes me think of some firmware or kernel bug :

The Android you have right before installation (34.3.A.0.228 or .238) is the latest Android Nougat 7.1.1 with the latest kernel at that moment (3.10.108 or something along this line) and the corresponding firmware is also that recent and up-to-date.

(NOTE: on Qualcomm chip, the baseband firmware play an important role, because the modem is part of the main chipset and is in charge of several low-level functions - which might include the SD cards, and which might even include RAM. There goes all your hope of privacy out of the window.)

Sailfish X uses a slightly older version of the kernel : 3.10.84, and the various binary firmware (the thing that you must download from Sony's web site during the Sailfish X installation) come too from the slightly older Android 6.0.1 Mashmallow.

It might be that either this kernel or one of the various binary firmwares is broken and somehow fails to initialise some uSDHC cards under some weird circumstance.

GOOD NEWS: ... if that's the case, that's some good news. It simply means that you have to wait until Jolla releases an update of Sailfish X that uses the slightly newer kernel and firmware that your Xperia X had right before the upgrade.
Or even better the upcoming kernel 4.4 that Sony is preparing as part of their Android 8.0 Oreo efforts.

(Which by itself is quite awesome : unlike Jolla 1, where Jolla Oy was basically alone and doesn't have the devs ressources / the influence to get an upgraded Kit-kat ready kernel+drivers set from Qualcomm (see threads on TJC),
in this case Sony has definitely all the necessary might and developers workforce to pull a kernel 4.4 - and are currently in the process of doing it)

Some general info :
"dmesg" is the old style command that has been available since ages.
"journalctl" is the systemd-specific modern equivalent (dmesg pulls from the same database).

... because all that quality is due to advanced proprietary post-processing done in software. That is the thing that is protected by the DRM keys stored in the TA.
(Which means that, once we have a solution to run at least Android 6.0 apps, we could in theory install Sony's App, the DRM keys that you backed up and enjoy the high quality post-processing)