Another alternative would be to use flashtool which works on Linux too (NOTE: requires access to raw USB port. So either udev rule or run as root if you're lazy).

Guide such as this one suggest http://xperiafirmware.com/ as a source of ROMs.XperiFirm would be another tool (might require a few extra step to repack the .ZIP file into a .FTF flashable file)

That's the tools I used back when Sailfish X came out to do all my flashing and TA backups (this howto even covers the "generate .FTF from XperiFirm" part).

Bonus point: if you happen to have saved your TA partition before unlocking the phone you would even be able to flash your backup and relock it as in from factory state (including the DRM and special Sony camera firmware bits).

But AFAIK, nobody on the forums has ever complained of warranty repairs *on the screen* being refused in case of missing TA partition.

Also, if I remember the latest European legislation evolution, the warranty of the device should cover screen repair, even if the currently fitted-in screen happens to be 3rd party, but I'm not 100% sure.
(More or less the same kind of question raised by the "right to repair" legislations in the US).
So maybe Sony Europe should be able to repair your screen if its still within the 2-years of legal european warranty.