IIRC the idea is to send a chain of probes at regular intervals, and the probes would relay signals back along the chain.

So, even less plausible than a solar-system-sized radio telescope.

According to https://en.wikipedia.org/wiki/Breakthrough_Starshot#Laser_da..., the probes should be able to talk to a 30-meter telescope on earth using lasers. The data rates are very low, of course, but that can be handled by making sure the probe has enough storage for its few-hour-long transit of the system and then transmitting that back over the following months.

How do they get the laser out there? What powers it?

From https://arxiv.org/ftp/arxiv/papers/2005/2005.08940.pdf

> The sailcraft transmits 100 Watts, deriving its power from a 700-Watt hydrogen beam that is normally incident on the sailcraft when it faces Earth. This hydrogen beam is simply a manifestation of the interstellar medium, incident on the sailcraft at 0.2 c.

From https://arxiv.org/pdf/1805.01306.pdf

> One way to tap the sailcraft’s kinetic energy could be via the interstellar medium: The Local Interstellar Cloud is primarily composed of 0.3 atoms/cm3 of partially ionized hydrogen. From the sailcraft’s perspective traveling at cruise velocity, this manifests as a monochromatic hydrogen beam that is incident from the direction of travel, having a combined kinetic energy of 55W m−2, or 0.7 kW over the sail’s area if it faces the direction of travel.

The report for Starlight suggests a RTG:

https://www.nasa.gov/sites/default/files/atoms/files/roadmap...

So you are bombarded by a mix of relativistic hydrogen atoms, molecules, nuclei, and electrons. How do you extract energy from such an influx? Will extracting it slow you down much?

Actually it would vaporize any part of the system needed to control or communicate.