First of all:
Rooting a device is not the same as making the device more privacy-friendly.
By the way: Rooting is not required to use /e/OS.
/e/OS is currently not an option for your Galaxy A34 5G SM-A346E because /e/OS does not support the SM-A346E (nor does the source code author LineageOS Android distribution) with a CustomROM.
Your Samsung Android 14 Firmware A346EXXS7CXE2 Bit/SW REV. 7 is not downgradable to Android 13 (because Samsung has implemented a rollback lock in the firmware) to be able to use the future /e/OS-T GSI
Currently, the only way to free your Galaxy A34 5G from the Xiaomi and Google ghosts is to install an Android 14 Open Source Project (AOSP 14) Generic System Image (GSI), but this cannot be done without know-how.
The very first step,
however, is to unlock the bootloader. This Xiaomi procedure requires at least 168 hours (7 days) waiting time from the application for unlocking.
Yes, this path is rocky, but it is worth it to counter the data theft by Xiaomi, Google and the tracker apps.