For Voyager, I'll argue that it's mission is much simpler (doesn't need to aim forthe position of something 30 years in the future) and that we keep transmitting to it (the sheer distance will limit our involvement as the delays between transmissions grows). It's also not going at 0.15c, where it needs to do the calcs very quickly.
I'm not sure how easy it would be to make a km wide Gw array on Earth, but building and powering it in space seems much, much harder. Just harvesting the GW takes 3 million solar panels. Just getting that to orbit seems unlikely. Even with very generous 1kg per panel we get 3 million kg to put in orbit, or 21 Falcon Heavy at max payload, or two years of putting nothing but solar panels up. It's so much.
And then how much money is going to make the gram scale probe appear?
Edit0: to clarify, the probe will have less time than the duration of the blink of an eye to take measurements. That's limiting what you can learn AND makes it very hard to aim correctly.
Betting against humans making breakthroughs is usually a bad bet. As the saying goes: "You can say 'it can't be done' all you want, but please stay out of the way of those who are doing it."!
Construct a stack of starships in orbit and you would be able to get a probe there. It’s never about the technology, it’s about whether someone cares enough to spend the resources.