The purpose of this answer is to counter the following comment from the OP [emphasis mine]:
Even with 3rd party tools, I am forced to use a 2K cluster size with FAT32 on a 250GB volume. I do not understand why that is, why no tool can do it with 1K clusters given the FAT32 limit as I understand it.
Testbed
$ cat /etc/issue
Ubuntu 21.10 \n \l
$ uname -a
Linux xxxxxx 5.13.0-20-generic #20-Ubuntu SMP Fri Oct 15 14:21:35 UTC 2021 x86_64 x86_64 x86_64 GNU/Linux
$ mkfs.fat 2>/dev/null
mkfs.fat 4.2 (2021-01-31)
No device specified.
Preparation
$ truncate -s 250G filesystem
$ wc -c filesystem
268435456000 filesystem
(Note 250G
means 250 GiB which is even bigger than 250 GB you had in mind. I have tested both sizes. This answer shows just one test for brevity.)
Filesystem creation
Deliberate attempt with cluster size of 512 bytes, to see what happens when the cluster size is really too small:
$ mkfs.fat -F 32 -S 512 -s 1 -v filesystem
mkfs.fat 4.2 (2021-01-31)
WARNING: Number of clusters for 32 bit FAT is less then suggested minimum.
mkfs.fat: Not enough or too many clusters for filesystem - try less or more sectors per cluster
With cluster size of 1024 bytes:
$ mkfs.fat -F 32 -S 512 -s 2 -v filesystem
mkfs.fat 4.2 (2021-01-31)
filesystem has 255 heads and 63 sectors per track,
hidden sectors 0x0000;
logical sector size is 512,
using 0xf8 media descriptor, with 524287953 sectors;
drive number 0x80;
filesystem has 2 32-bit FATs and 2 sectors per cluster.
FAT size is 2032124 sectors, and provides 260111836 clusters.
There are 32 reserved sectors.
Volume ID is 46a16c4f, no volume label.
$ echo $?
0
Verification
$ file filesystem
filesystem: DOS/MBR boot sector, code offset 0x58+2, OEM-ID "mkfs.fat", sectors/cluster 2, Media descriptor 0xf8, sectors/track 63, heads 255, FAT (32 bit), sectors/FAT 2032124, serial number 0x46a16c4f, unlabeled
$ sudo mount filesystem /mnt/tmp
$ echo $?
0
Conclusions
The 3rd party tools you tried may be arbitrarily limited (like Windows, possibly to a smaller degree but still). The claim "no tool can do it with 1K clusters" is unjustified, mkfs.fat
in Linux can.