Check the trigger bar to firing pin engagement. That's the last link in the multi engagement sear mechanism.
If the trigger bar isn't holding the firingpin in the cocked position as the breech slams shut, the firing pin drops off of the trigger bar and fires the chambered round at that moment and the cycle starts all over again,,F/A fire.
The trigger bar spring (flat spring) could be too light weight (replacement)
There could be debris under the sear bar in it's cavity in the frame not allowing it to seat deep enough. The result is it can't engage the firing pin fully.
The small trigger bar plunger and spring at the front end of the trigger bar might not be working. That's the disconnector of the system and allows the trigger bar to jump back and re-engage the sear edge on the firing pin after a shot.
The sear edge itself on the bar may be worn over (not sharp or shaped correctly) and unable to hold the firing pin securely.
The firing pin has a very shallow opposing sear edge on it's left side that the sear bar engages. Also check that sear edge for wear, chips, damage or alteration. The firing pin should have a ser# on it matching the pistol frame if orig.
Remove the FP by pushing in the FP bushing/guide with a screwdriver placed in the slot in the bushing,,turn the bushing 1/4 turn to release it against the spring tension and allow the bushing, coil spring and the Firing pin itself to back out of the breech block.
(The screwdriver blade tip on the Luger loading tool was for this)
You can check some what to see if these sear edges and springs are OK by doing the following.
WITH THE PISTOL UNLOADED>>
Remove the magazine
Pull the toggle breech all the way to the rear to cock the pistol and let the toggle down easy. Confirm that the pistol does in fact cock by dry firing it. (one of the few times I would dry fire a gun).
Now do the same operation cocking the pistol but this time let the toggle snap forward with it's spring tension alone driving it.,,Let it slam forward and home on it's own.
Now see if that slam forward has left the pistol cocked (will it dry fire?) or is the pistol now uncocked? (the slam of the breech fired the pistol by knocking the triggerbar & trigger out of engagment from the impact).
Try it a few times to confirm, but still inspect the parts above even if it doesn't jump off the sear bar.
That's about all I can think of right now on long distance.