I haven't used a trainer in over forty years (a MEK 6800D2), and it had a ROM monitor which included a TTY uploader for Motorola format paper tapes, but it was in no sense a bootloader because the start address of the uploaded code still had to be manually entered on the keypad, and the "go" key hit.
As a student, I even wrote monitor extensions to interface to an optical tape reader to allow faster uploads.
I think my supervisor would have failed me if I'd referred to it as "an OS"