Buildroot and Ideas...

Okay. So, I am going to make some notes here to help you, me, and anyone else looking over these items of interest.

wget https://toolchains.bootlin.com/downloads/releases/toolchains/armv7-eabihf/tarballs/armv7-eabihf--glibc--bleeding-edge-2021.11-1.tar.bz2

tar -xvf armv7-eabihf--glibc--bleeding-edge-2021.11-1
cd u-boot
make ARCH=arm CROSS_COMPILE=~/YOUR_DIR/armv7-eabihf--glibc--bleeding-edge-2021.11-1/bin/arm-buildroot-linux-gnueabihf- distclean
make ARCH=arm CROSS_COMPILE=~/YOUR_DIR/armv7-eabihf--glibc--bleeding-edge-2021.11-1/bin/arm-buildroot-linux-gnueabihf- am335x_evm_defconfig
make ARCH=arm CROSS_COMPILE=~/YOUR_DIR/armv7-eabihf--glibc--bleeding-edge-2021.11-1/bin/arm-buildroot-linux-gnueabihf- menuconfig if needed?

Go to / in the u-boot prompt
Type in CMD_EXTENSION
Find in the GUI where exactly CMD_EXTENSION is located in the menuconfig
We need to have CONFIG_EXENTION_CMD=y and we can now build u-boot
make ARCH=arm CROSS_COMPILE=~/YOUR_DIR/armv7-eabihf--glibc--bleeding-edge-2021.11-1/bin/arm-buildroot-linux-gnueabihf-
cp MLO u-boot.img /media/$USER/boot/

Now, for the building of zImage, dtbs, and modules...

wget https://cdn.kernel.org/pub/linux/kernel/v5.x/linux-5.4.197.tar.xz

tar -xvf linux-5.4.197.tar.xz
cd linux-5.4.197
make ARCH=arm CROSS_COMPILE=~/YOUR_DIR/armv7-eabihf--glibc--bleeding-edge-2021.11-1/bin/arm-buildroot-linux-gnueabihf- omap2plus_defconfig
make ARCH=arm CROSS_COMPILE=~/YOUR_DIR/armv7-eabihf--glibc--bleeding-edge-2021.11-1/bin/arm-buildroot-linux-gnueabihf- menuconfig if needed?

Within the GUI find, by /, OF_OVERLAY.
a. Also, the rootfs.cpio build needs to be put in INITRAMFS_SOURCE by searching with /
b. So, something like ../rootfs.cpio goes in the box in the GUI after the download
make ARCH=arm CROSS_COMPILE=YOUR_DIR/armv7-eabihf--glibc--bleeding-edge-2021.11-1/bin/arm-buildroot-linux-gnueabihf- zImage modules dtbs
cp zImage /media/$USER/boot/
zImage can be found once the kernel has been built in /arch/arm/boot/
cp am335x-boneblack.dtb /media/$USER/boot/
am335x-boneblack.dtb can be found in /arch/arm/boot/dts/

Now, if anyone wants to chime in here, please do. B/c, for some reason, I have not got this specific build to work just yet.
Seth
P.S. Everything builds correctly but I think my toolchain is outdated. For Bullseye, there is an updated gcc for cross-compilation. Anyway...this is the update so far. It may or may not work due to dependencies.
OKAY. I see what works and does not work so far. With the current bleeding-edge toolchain from bootlin, their respective kernel to use, I THINK, is 5.4.x and u-boot needs to be newer than the kernel. BUT...the info. here, https://beagleboard.org/blog/2022-06-06-using-the-u-boot-extension-board-manager-beaglebone-boards-example, was not ported to u-boot until very recently b/c of beagleboard.org.

@gpioblink ,
Hello Again...Seth here. So, I think in fact it is the course of the partition making that is in the way.
I have done some research and I think using /dev/mmcblk1 for instance over /dev/sda1 for instance is preferable.
I will test tonight and reply once I configure something worth sharing.
Seth
P.S. If you have made it past this phase in your development, please disregard what I am typing. This link says differently, https://forum.digikey.com/t/debian-getting-started-with-the-beaglebone-black/12967 . So, I will keep trying to support this cause. BBL! https://toolchains.bootlin.com/ may help too...

Okay...so.
In Buildroot, try to use these commands:

cd buildroot
cd configs
nano BONE_defconfig
C & P https://bootlin.com/pub/2022/u-boot-extension-mgr/src/buildroot-2021.02.5.config in BONE_defconfig
make ARCH=arm CROSS_COMPILE=your_toolchain BONE_defconfig
go to /buildroot/output/images/
There should be a bunch of files for your disposal
Add those files to the /boot and /rootfs files in your partitioned SD Card.
WIP

I am still working on the finalization of this process. Bear w/ me.
Seth
P.S. Okay, so. I now have a rootfs file to show off but I am not sure exactly what to do w/ it thus far: