If we’re talking about human technology available in a few hundred years, don’t discount far more exotic options. I’ve heard people talk of theoretical terrestrial lasers pushing on tiny probes. With an absolutely gigantic laser and magical material at the back of the probe that won’t instantly vaporize there’s enough energy to get something the size of a smartphone up to a reasonable proportion of the speed of light.
I can’t prescribe this theoretical technology to the problem. But I also think it’s unreasonable to set the limit using known technology and then discount the idea altogether. We have no idea what will be possible in 300 years.
Exactly. Imagine what would be possible after a billion year of technological evolution, heck even just 100'000 years. We already know that space time metric engineering is theoretically possible within our current understanding of physics, we don't have either the technology or access to energy density necessary to do it. And that's only within our limited understanding of how the universe works.
Note that you can't use these lasers to slow down the probe, which will dramatically limit the things the probe can do at the destination. I'm not even sure what kind of interesting things a probe the size of a smartphone could do, let alone phone home.
send an unending chain of them and you solve the transmission problem _and_ they don't have to slow down as you'll always have another on the way past whatever you're targeting