Please be careful with flashing a custom u-boot to eMMC of imx8mp. Flashing a non-working u-boot may soft brick your device. In case this happens, unbricking it is a bit more involved: Flashing eMMC Bootloader / Unbricking (IMX8MP)
Originally, flashing a different u-boot wasn’t even a thing that was considered to be a feature by MNT unless you really, really, really knew what you were doing: 2024-08-04.log
That’s why for a long time, reform-flash-uboot would completely disallow flashing u-boot on imx8mp. These days, it will let you flash it but only if the hash matches the known latest one and even then only with a big fat warning.
Even with the stock u-boot on eMMC, that u-boot will first try to read boot.scr or extlinux.conf from the first partition of your sd-card. It does not matter that u-boot is on eMMC. The sd-card will be tried first. It does not matter where your u-boot got loaded from and imx8mp cannot load u-boot from your sd-card. So if the stock u-boot does not load your system on sd-card, then you might’ve misconfigured boot.scr or extlinux.conf on your sd-card.
You probably have a UART adapter to figure out what is going on early in the boot process? If yes, please post some output so that we can figure out why it still boots your system on eMMC instead of your system on sd-card. If no, I would really not recommend you flash your custom u-boot image to emmc…