What accounts for the fact that Polaris has drawn closer to the direction of true magnetic north?

Motion and speed are relative terms. Asking how fast you are traveling immediately begs the question "relative to what?" In a car that is traveling down the road, you might be moving at 45 miles per hour relative to the road, but you aren't moving at all relative to the car's trunk. Star position and movement is similar in this regard. Stars appear to change position over the course of a night or season because of Earth's rotation around its axis and revolution around the sun. A star like Polaris is visible all year from the northern hemisphere, but that doesn't mean it appears completely stationary. The Earth is on the opposite side of its orbit about every 180 days. This change in Earth's position will cause celestial objects to appear to shift around a little bit. This is called parallax. You can easily demonstrate it by holding your thumb up in front of your face at arm's length. Close one eye. Then quickly alternate back and forth which eye is closed. Your thumb will appear to shift and wiggle back and forth even though it's not moving at all. Polaris is subject to this kind of apparent motion. Additionally, Polaris is actually moving. Polaris exists in the Milky Way, and our galaxy is not static. It rotates and is moving through the vastness of space. Polaris is subject to all of this motion. The fact that Polaris is moving closer to magnetic north or geographic north is coincidental.
One final note. While it's true that Polaris and Earth's magnetic north are falling closer in line, it's also true that Earth's magnetic field is constantly changing. It's possible that Earth's magnetic north is moving closer to Polaris's position and not the other way around.
https://earthsky.org/astronomy-essentials/north-star-movement