I think we can all but rule out a dead, ancient planet-spanning civilization on Mars now. We have medium resolution imagery of the entire planet and high resolution (meter or submeter) imagery of a lot of the surface, in a wide distribution. Mars hasn’t had enough volcanic activity to hide evidence of a planet-spanning civilization unless it occurred while large asteroid impacts were much more common.

Venus, however, is sheathed in clouds. So we only have low resolution radar images of most of the planet, and we’ve only sent a few very short-lived landers with low resolution cameras to the surface. They could have landed in areas that were once oceans or otherwise uninhabited. And secondly, Venus has been basically completely resurfaced with lava over time. Venus may once have had large oceans before runaway greenhouse effect. (And keep in mind that the Sun has gotten significantly brighter over billions of years, besides the increased greenhouse effect on Venus.) And so we can’t even rule out a planet-spanning civilization like our own. It’d take a lot more exploration and drilling to rule that out.

A planet spanning civilization on Mars is less likely. However, there are still ways it could be found, depending on how long ago it was. I list three ways below, and suspect there are more.

First, there is the possibility of a civilization dying and evidence being erased by tectonic plate recycling. Mars is approximately 4.6 billion years old. We know it has volcanic activity, and most consider it to have inactive tectonics now. Some scientists believe it could have had significant activity in the past, based on the 3 distinct regions of Mars. Earth's tectonic plates vary in their rates of recycling: the oldest non-oceanic tectonic plate is 3.6 billion years old, and shows no sign of recycling. Oceanic plates recycle on the average of every 180 million years though.

Second, there is the possibility of technology that didn't leave a visible trace. This is not supported by any evidence and is mere conjecture. If the society tore down non-organic structures and converted to using all biodegradable/organic materials then evidence of the society would be scarce, if existent at all, especially if bodies were cremated as many do today. Chemical analysis could detect this I suspect, or more importantly prove it wrong.

Last, if for some reason civilization evolved underground and stayed underground, then there wouldn't be any visible evidence above ground. This is also pure conjecture. Micro-robots that explore Mars' caves might find something, as might ground penetrating radar.

Mars has volcanism but not tectonic plate recycling. That’s an Earth thing. There are large parts of the surface of Mars that are MUCH older than any significant surface areas of the Earth for this reason. And that’s my point.

I always wondered what it would be like if Mars and Venus were swapped. Would Mars be warmer, or would it be even more devoid of atmosphere? And would Venus (with its greenhouse gas) be a more livable temperature if it was in Mars's orbit? It still wouldn't be survivable due to the atmospheric composition, but I was just wondering about raw climate.

Yes, mars is too small to hold its atmosphere at its current distance from the sun, moving it closer would only make the problem worse. Like our moon, the bright side would be hot during the day, but it would be cold at night with very little atmosphere to retain heat, and even in temperate regions at the poles liquid water would not be stable.

We're not really sure what kicked off Venus' runaway greenhouse, so it's possible that would still occur, though it does seem less likely. Without the runaway greenhouse, Venus' atmosphere would likely remain primarily nitrogen. Its atmosphere would still be significantly thicker than Earth's but by a factor of 5 instead of a factor of 100. With the additional atmosphere, it might remain quite temperate even at the greater distance.

Of course had Venus and Mars developed in eachother's places, Venus would have developed as a smaller world with a thinner atmosphere (generally more mars-like) and Mars would have been larger with a thicker atmosphere (generally more venus-like), so the whole point is somewhat moot.

The atmospheric composition is likely driven in part by the higher intensity of the Sun. At Mars, it’d have gotten a quarter of the sunlight. That means more water in its atmosphere (as there’s have been less UV to dissociate the water and less light pressure and less solar wind to blow the hydrogen away), less release of CO2 from carbonates, etc.

As far as your latter point about life spreading, what’s interesting to me is that the most strict interpretation of our “planetary protection” guidelines at NASA actually prohibit life spreading to other worlds.

Red Tape as the real Great Filter...

It would not surprise me if civilizations evolved in the same way life did on Earth.

Life evolved in the sea. At some point life evolved to leave the sea and go to land, whether the sea was no longer hospitable enough, or in search of better food. Life continued to evolve on Land, specializing into different groups and colonizing different lands.

Perhaps civilizations evolve on their planet, then at some point they leave their planet and go into space (when their planet is no longer hospitable or they need more/better food). Finally, while in space they evolve more, founding different colonies that evolve differently due to culture and environmental differences.

This sounds like a lot of wishful thinking.

The most probable scenario is that life is born multiple times, in multiple places, when conditions permit it.

There's no evidence of life moving across planets of different star systems.