The LVGL lv_fs_fatsfs (which is used by LVGL for filesystem-operations when you select FATFS in lv_conf.h) has an lv_fs_fatfs_init function called internally by lv_init() at startup. This assigns the open/read/etc. functions to the FatFS library by default. But this library is a generic FAT32/exFAT library and can’t use the SD-card directly. To mount and use the SD-card by it would take configuration that’s covered by FatFS’s own documentation, maybe you can use it together with the SD library somehow.
But the SD library which you’d like to use seems to have the mounting and FAT filesystem support already built in, so you might follow an easier path by not using the preconfigured FATFS in lv_conf.h but registering the SD.open/read/etc. functions of the SD library to a new lv_fs_drv_t and give it the drive letter as seen in the linked LVGL-document example at File system — LVGL documentation.
There’s another forum topic covering this use-case where I answered nearly the same: Upload Image C array file from SD Card - #5 by dbtronics
For further info and more specific examples you can follow the LVGL forum, for example: How do I correctly make the SD Card work for image widgets on an ESP32 Dev Kit with LVGL v.8.3? - How-to - LVGL Forum