Did you clean those terminals before you put it all back together?
In my auto fixing history I have done a number of starters but not on an m54.
The solenoid has wiring that energizes it to push the starter gear into the gear on the back end of the motor. Flywheel on a stick shift flex plate(?) on an automatic.
When the started motor just spins, the solenoid isn't being engaged. You can try tapping on it to get it unstuck. My suspicion is that you have a small wire issue in the wires that activate the solenoid. I have my motor torn apart about like what's in your photo if you want anything checked, let me know. Or photos...
Can you stand on your head and get multimeter readings to see if you have power to the solenoid or jumper it to see if it goes?

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2001 x5 3.0 (sold with broken motor), 1990 e30 M3, 1991 318is, 2002 325i, 2008 335i Dinan stage 3 6 speed,