To save someone two seconds of searching,

NASA animation of Voyager 2's trajectory (time in the bottom-left corner): https://youtu.be/l8TA7BU2Bvo

This is great. I did not realize Voyager 2 also left the ecliptic at the end of its tour.

That happened because Voyager 2 went over Neptune's north pole rather than an equatorial trajectory. Both to get a look at a giant planet's polar regions, and because that would get it closest to the moon Triton. So Voyager 2's trajectory got bent southward out of the ecliptic plane as a result of that.

While I'm here: why didn't Voyager 2 continue to slingshot to Pluto? The answer is that its trajectory would have had to bend by about 90° at Neptune, which would have required an apex closer to Neptune's center of mass than the planet's own radius - it would have crashed into the planet instead.

How much do/can they use their own thrusters to change/correct their directions? I'm guessing it's just fractions of a degree? And needs to be extremely precise, done weeks? before reaching the next planet to slingshot around?

The Voyager probes were built with many course corrections and maneuvers in mind. They carried 100kg of Hydrazine fuel at launch, and it is almost all used up. That was about 1/8th of total craft mass at launch, which is significant.

Midcourse corrections are a standard and planned part of lots of probe missions.

I think we even did midcourse corrections for the moon missions.

A few degrees is probably the order of magnitude, though I haven't seen hard numbers.

I know that space is incredibly empty, but the vast expanse of space just boggles my mind so much. Even a slight miscalculation could have meant that the spacecraft hit that massive grid rotating around the orbit of Neptune.

There isn’t much value in gravity assists from Uranus or Neptune since they move much more slowly than Jupiter and Saturn.

Yes, but the trajectory change was also needed at Uranus. It’s not only about magnitude, it’s also about direction :)