Space

Also, probably nobody capable of traveling the stars wants to settle a planet. Once you figure out how to make huge spaceships (which you’ll need to travel interstellar space) you’ve essentially learned how to make cities in space.

I don't think it is a valid point. Yeah, if we can build a ship that take us to Alpha Centauri it would lool like a small city, but that does not mean that it can last forever and the traveller would never need to settle on a planet. And looking what the humans did in the past, it seems logic that while a part would want to continue to explore, another part would want to settle on a planet.

Our solar system would support a lot of people if we just used the resources available for space habitats, and by “lot” I mean in the quadrillions. And it turns out that all you need to support that population is a star to provide energy, and some planets to source materials from.

So with that in mind, why bother finding another habitable planet?

Because it is habitable and can be used as a transit point, advanced outpost, refuelling base or any other use you can do of an habitable planet where to do things you have not to fight even with the environment (tourism for example).

The thing is, out of a population of trillions (or even quadrillions as you say), you only need a few thousand to travel to the stars to colonize another planet. With how large the population is, that is bound to happen. Just like there were bound to be pioneers travelling to the new world to settle it, despite how dangerous the journey was. And how there will be pioneers to settle the moon or mars or further out.

And a civilization like that would absolutely send stuff to other star systems, if only for science, so most of the research for the journey would already be done. And this is assuming that a civilization wouldn't want ever greater quantities of resources for ever greater projects, or access to other star systems for reasons we cannot fathom today (maybe neutron stars or black holes have some incredibly tempting uses? Or maybe there's some useful resources out in the galaxy that we have yet to discover?)

Basically, a successful civilization like that is bound to spread out, it's difficult to see scenarios where a successful civilization would be so homogenous in thought as for that to not happen. Amd then it's before we even get to sending AI probes to "colonize" space and gather data.

Suhweeet! We can be the Old Ones, Chutulu flatghn la!

Or there are plenty of societies at least as advanced as we are, but we can't find each other because space is big and our stars tend to drown out our own puny EM emissions.