Farid,
Can you post the boot logs related to the flashing of the eMMC(UART output when flashing is initiated in DFU mode).
From the information you provided, it looks like the interface between OSD32MP1 and eMMC is functional.
As you are able to get to u-boot, the first thing to check is whether the boot mode is correct. If you execute “md.l 0x50020000 1” in u-boot command line, it should tell you what the device thinks the boot mode configuration is(See SYSCFG_BOOTR register description in the Technical Reference Manual - RM0436).
As you have access to u-boot command line, you can run the command “run distro_bootcmd” to see if the board can use the eMMC to boot the rest of the way. If eMMC is flashed correctly for boot and rootfs partitions, it should boot to Linux command line with eMMC rootfile system.
It eMMC is programmed and the board boots correctly after executing distro_bootcmd, there may be an issue is the boot0 and boot1 partitions of the eMMC. Booting from eMMC depends on FSBL being programmed into mmcblk2boot0 and mmcblk2boot1 partitions of eMMC that are apart from the main eMMC partitions. These are marked read only by default, but needed for eMMC boot.
Once you are are in Linux command line, you can program the boot0 and boot1 partitions like shown here: https://octavosystems.com/forums/topic/cloning-emmc-2/.
Best,
Neeraj