I have just successfully installed eOS on my Galaxy S10e and would like to report on my experience. I am not an expert, just a normal user.
My S10e (SM-G970F) was running after the last update on version Android 12/DEC 2022, UI version 4.1., Buildno. …G970FXXUGHVJ5. In this version, it was not possible for me to install eOS. After the last reboot nothing worked, but luckily still the download mode!
Thanks to great support by this forum and tips on XDA-Forum, I installed an earlier version of Android 12 (27.9.2022), found in a spanish version (my was german). The key was to find an earlier version in Bit G. Runnig the setup it was no problem changing into my language or any other. It is important to do the reboot with WiFi switched on and to switch off the automatic update as soon as possible. Then wait until the (minimally) setup is complete so that for later use the OEM setting is present in the developer options.
All firmware files ended with …GHVI4. example: AP_G970FXXSGHVI4. In this version it then was possible to install eOS without any problems.
I got the firmware on samfw.com.