Back-up your ROMs/BIOS/Configs via file shares from you exiting Pi 3 installation - see https://retropie.org.uk/docs/Updating-RetroPie/#making-a-backup-option-2, then install/flash the new Pi 4 image on the SD card. After installation restore the files you backed up in the previous step using file shares to the same locations (BIOS/ROMS/configs).
It's always advisable to make a backup of your existing installation, but you already did this,