It appears the slide stop has been modified or from a different make. I don't have a M52 anymore so can't compare.
The picture below is my 39-nothing. I hope it comes out clear enough so you can see what the engagement and slide stop should look like. As you can see the slide stop has a tapered point on it that engages the follower. Yours appears to be flat. It's definitely not long enough. With the slide stop inserted and if you push down on the thumb piece the follower should move down a bit. Yours is not engaging because it's too short.
Hopefully if you can find another slide stop that should fix you up.

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183rd FBINA