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Well, it’s own doc says the OS occupies 2 sectors, IOW > 512 bytes. Doing all those system calls in less than 1K is still impressive though.

Says 512 bytes of machine code, not "fits in the MBR". You can only cram 355 or so bytes of code into MBR area designated for that.

If you're fine with overwriting the partition table, you can go up to 510 bytes of code, followed by 2 bytes for the mandatory MBR boot signature

No partition table on floppy disks.