A solar gravitational lens will be humanity's most powerful telescope (2022)

Is this a similar principle to the concept in the 3 Body Problem series of books? As in, how one of the main characters is able to boost the transmission power of an earth bound antenna

From my layman understanding, yes, this concept should be bidirectional.

It's not a way to boost a signal.

It's using the Sun as a (gravity) lens, with probes at the focal point to gather the image. Because it's a very large lens, that's allow to have a massive zoom on whatever object we are interested in.

In the three body problem she uses some property of the Sun's internal layers to amplify the signal. In reality we don't know of any actual property in the Sun that could do this.

The gravitational lens idea is different, it makes use of a known phenomenom where the Sun's gravity "bends" light rays moving around it, which can amplify the light coming from far away objects. In principle you could run it backwards, so the lens could amplify signals we send as well.

But you should be able to use it as a "parabolic" mirror, to make a very directed ray to the planet. (Assuming diffraction is not a problem.) (Assuming no time delay, because to see the planet you should look to were it was many years ago, but to send a message you should aim to where it will be many years in the future.) (Assuming I'm not missing a few more technical problems that are not impossible to solve, but extremely difficult.)

Wouldn't you have to have very accurate information about where the planet is going to be when the light arrives?

The ability to observe at given resolution implies though that there is a lightcone of civilization discovery spreading from humanity, visible to our neighbours.

It wouldn't amplify them, there's no energy gain. A gravitational lenses just bends the trajectory of the waves. If you do it right it may be possible to use that to focus the signal on a directional trajectory(as in, the same energy is redirected in a single direction instead of being spread out), if I'm not mistaken.