I have similar side plate movement on one Model 1900 Luger, a worn shooter. I suspect the wear was caused mostly by rust which was then removed via abrasion, the pistol has probably been refinished several times.
Not only did the side plate move under trigger pressure, but the fit of the upper onto the lower was so loose that even with the safety on, the sear bar would move enough to allow the weapon to be fired. More concerning was the fact that the looseness occasionally caused more than one round to be fired on a single trigger pull (sear bar/firing pin contact must have been too light/too loose).
I had my gunsmith make two small welds to add metal to the upper to reduce play. Now the safety operates correctly and I'm comfortable that everything is sufficiently tight to prevent multiple discharges from a single pull. And side plate movement is reduced.
On my nicer collectibles there is zero movement of the side plate under trigger pressure.
From all this I conclude that as a Luger wears side plates and other parts may exhibit movement. The effect on performance is progressive - some degree of movement does not impede function, but eventually it can reach a point where the parts have too much play and function degrades. Any Luger with loose parts should be carefully inspected by someone who understands Luger operation to verify adequate parts function and that the weapon is safe to fire.
My 2 cents.
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