Why aren’t these Shimano PD-M980 coming apart?
Problem solved! I realized that the sleeve should not be able to press itself up the spindle like it did in photo #2. I clamped a set of vice grip pliers between the sleeve and the spindle’s flange to stop it from press-fitting itself into the spindle. It came out after that. I will inspect the whole assembly for damage since the hardened steel spindle is significantly larger than the aluminum sleeve.
Edit:
To conclude this saga, the bearing disassembled itself while still pressed into the pedal body, which is terminal. There is no way to remove the bearing cup, which was supposed to be press-fit in and out via the black threaded sleeve. It was worth a try though!