Can a runway at an international airport become misaligned like this?

Ok so. A runway 04 has is found between 036 and 045 on a compass. But can it 046 on a compass and still be numbered 04?

I'm not talking about small airstrips. I'm talking about small + mid sized to huge airports. Ones where you would see A320s and 737s.

I'm a plane spotter and love to flight sim. I'm not a pilot I know. It's just I was looking at a chart for LFMN. That has 2 runways 04L and 04R. But both are aligned 046.
Does this occur in the real world?

YES IT DOES. The runways 7L -25R and 7R-25L at KPHX are that way. They should theoretically be renumbered 8-26 because of magnetic drift over the years but the change apparently would be too disruptive to institute at the present time.

Perhaps the runway was resurfaced and became farther tilted from 040 because of soil conditions or some other reason.
Your angles might be by true cardinal point directions or by magnetic? Magnetic does not stay constant, but might vary over time. The runway might have been labeled at a time when magnetic was different, or is really very close to 040 true?

YES it happens. There are too many places that need to be updated for this minor rounding difference.
Do you expect every map on the planet of Airports to be replaced. 45,000 airports on the planet.
Millions of maps.
They sometimes will be renumbered when they are modified. For example new flight paths new radar beacons or whatever.

REAL planes unlike your game use many reference points to get the plane to the end of the runway.
The pilot actually uses his brain and eyes to nudge the plane left or right as needed.

At a large Airport with instrument landing the flight path radar directs the plane within about a dozen feet of centre line a few hundred yards from the end of runway.

It can be done visually with an arrangement of colored lights.

HINT the pilot is watching the lights NOT HIS COMPASS.

Get up a map of Hartsfield-Jackson Atlanta International Airport and examine it.

It has 5 runways, all parallel.
The are numbered 8L/26R, 8R/26L, 9L/26R, 9R/26L and 10/28.

That means that the "official" orientation of the 8L/26R is 20 degree off from 10/28.
But they are actually parallel.
So they are DELIBERATELY miss-numbered, by 10 full degree at least.

Runway numbers are a bit arbitrary, especially with multiple parallel runways, usually within 10 degrees of a heading. A tower clears you to land on runway 11L and the runway marked 18, time to think where you are.

Yes, that can often happen. Magnetic headings change continually because of the migration of the magnetic poles, but it's too little to do anything about frequently. There are far too many publications, charts etc. To do that with. Frankly, the runway number is simply a name, it doesn't state that it is the actual heading. Our runway recently officially became 32 instead of 31, it's still the same runway.

The more numbers the smaller they have to be. So lets say they use exact heading. The runway would be marked 245. If they have to add L and R then you got four characters on the runway. Usually they drop off the last number, so it would be 24L and 24R. If you have two airports close by they will fudge the numbers so they are not exact matches.