My complicated plan is to screw a plank onto the wall and mount the striker onto this..

Sorry I broke your brain because I wrote latch instead of striker.

The 2ft plank will disburse impact joules across a big surface so it will protect the sheetrock. And it's 2 ft because you'll find a stud within 2 ft to mount it to.

The plank adds material the strikerscrews can firmly grip. But the width of the added material will make it impossible for latch to catch striker since striker will now stop 1 plank width in front of latch.

So you inversely mount striker so that striker bends towards latch and therefore negates added material.

This is why you picked out plank width same as height difference between striker bend and striker mountpad

Carve out the curvature of the striker mount if you need the catching point to be exactly the same as before.

Add folded paper underneath plank if you need to make outwards micro adjustments to the catching moment.

The goal of the adjustments are to make the weight of the door slam into the doorframe, not the striker.

Rusty screws are not a problem because it's inside. Paper shims will not soak up water it's inside. (OP said it's inside the house and there's carpetted stairs in the picture ffs)

Screws will not snap off since I adviced to adjust the catching moment of striker in such a manner that the doorframe catches the door, not the striker.

Nope.

Drywall screws to screw the wood to the stud, paper to level out so that the door catches on the door frame and not on the latch.

It doesn't need to be more than that.

Problem: screws don't hold because of lack of material strength screws grab onto

Solution add more material.

2 dollar solution:

1. Measure distance between outer edge of latch and wall at point where lock catches latch.

2. Remove latch from wall

3. Buy 2 ft long plank that has a thickness of step 1. Buy 10 drywall screws.

4. Horizontally attach wood to wall with screws. Allign edge of wood with edge of wall. Allign middle of plank with point at which latch catches.

5. Screw the latch onto the plank upside down.

6. Check if door closes correctly. If it does you're done. If not see 7.

7. If door don't fully close you take a knife and notch out room on the plank for the bulge of the latch to fall into. If the door closes before latch catches you need to unscrew the plank and add folded paper to the edge of the wall and screw plank back into position.