cd /storage/.update
wget https://releases.libreelec.tv/LibreELEC-Generic.x86_64-10.0.3.tar
cd /storage
systemctl stop kodi
mv /storage/.kodi /storage/.kodi-old
reboot
If the current install boots/runs fine check the size of the boot partition. If it is ~230MB it's too small for a direct update to LE10 and you will need to figure out the install issue; hint, if you see the installer it's not a BIOS/EFI issue as it booted the installer. If it is ~512MB size the boot folder is large enough for a direct update. The commands above ^ download the LE 10.0.03 update file to the right place in preparation for a direct update. Then you stop Kodi, move the existing install files out of the way, and reboot to start the update. Once the update completes you will have a clean Kodi instance. You can then stop Kodi, copy essential bits of the old install from /storage/.kodi-old to /storage/.kodi (sources.xml, specific add-on settings, etc.) then restart Kodi to continue with setup. Rinse/repeat until things are as you need them again.
NB: Instructions saying you need to clean install for LE10 are not quite true. The OS and Kodi update with zero issues, but add-ons can cause major issues due to the Python 2 > Python 3 change. The process above avoids that by moving the old (and potentially problem) Kodi data including add-ons out of the way.