You can try using Patrick Gaskin's Kobo Firmware Downloads page to download the 4.38.21908 firmware for a Kobo Glo (the Mini and the Glo are Kobo4 hardware revision). Unpack the firmware .zip file and copy the contents (the upgrade directory and the KoboRoot.tgz and manifest.md5sum files) to the .kobo directory on your Mini. When you safely eject, the firmware should install. I have not tested any later firmware revisions on a Mini so you could try 4.38.23038 or 4.38.23171 and let me know how it went.
If you are not already on 3.19.5761-s or later, I would suggest installing that version first and then going to a 4.38.xxxxx firmware revision.
Kobo4 4.38.21908 link:
https://ereaderfiles.kobo.com/firmwares/kobo4/Aug2023/kobo-update-4.38.21908.zip
Kobo4 3.19.5761-s link:
https://ereaderfiles.kobo.com/firmwares/kobo4/january2016/kobo-update-3.19.5761-s.zip