A planet like Earth we'd be able to see clear across the galaxy, if we happened to look in the right direction.
If you are a physicist then how powerful a signal on how big an antenna would it take for us to hear the signal from the nearest star. Why do you think we would be able to see an earth sized planet near a Sol sized sun halfway across the galaxy? We are only just now able to see jupiter sized planets and I think those are only a few hundred light years away.
What is really needed for a civilization to move to the stars are barely sub-light ships and a way to absorb the momentum from your starship at each end of your trip so that it can be re-used. A large ring around a solar system like a particle accelerator that can shoot your ships to another system and at that other system have a ring ready to catch your ships.
A group called "The Living Universe Foundation" got started from a novel called "The Millenium Project" or something like that by a guy named Savage. In his book he has an 8 step program to seeding the galaxy with humans.
There are a number of unspecified parameters there, such as the frequency, bandwidth and isotropy of the signal, but according to my calculation, Arecibo would be able to hear a 100 megawatt radio signal on Alpha Centauri (if it could point in that direction, which it can't). The Earth pumps out much more than 100 megawatts of RF.
Why do you think we would be able to see an earth sized planet near a Sol sized sun halfway across the galaxy? We are only just now able to see jupiter sized planets and I think those are only a few hundred light years away.
There are lots of ways to "see" across the galaxy. We were talking about radio communications, not about optical imaging.