Interesting to think what conclusions would be drawn in these scenarios. Obviously atmospheric composition has drastically changed over the eons - I wonder what sort of civilization could detect these kind of longterm changes, and if they wouldn't have better observational capabilities than what we assume here given they have persistent knowledge over "long" timespans
Oxygen however. Just the fact that our atmosphere is as far out of equilibrium as it is.
They might notice a change in our atmosphere's composition, but honestly a 200 ppm to 400 ppm change of some trace gas over the course of two hundred years could have many much simpler explanations than "intelligent life dug up all the carbon and burned it".
At some point between 50 and 100 light years the Omni directional radio waves blend with the background radiation.
I have seen projections of "plausibly easy" detection up to 50 light years. They difference between the number of stars that are 50 light years vs 40 light years is about 2x, so the calculation of how many stars are in range is actually very sensitive to emission range. There are 64 stars 50 ly out, and almost 500 up to 100ly out.
That's still not that many though, given the 500 billion stars in our galaxy. It seems only plausible that an ET intelligence would detect us if they have seeded the galaxy with probes - in which case their would probably be one listening in our own system anyway.
Some people start longer discussions ("ragchews") from there. Though this is more common in regional communication. Topics can be all kinds of things, like exciting new ham radio topics ("there's a new ham radio satellite going up!"), where they've travelled (especially nice if you've been where the other person lives), their life history, health (not dead yet! me neither!) etc. Lots of random small talk. The main rule is to stay away from anything that could cause disagreement, like politics and religion.
This may not sound terribly interesting, but keep in mind that for many, this is really just the last step after a lot of time spent e.g. building and setting up new equipment or whatever. Also depending on propagation conditions (which vary wildly), just understanding the other person is a challenge in itself. The actual talking is often more of a side benefit.
Above is mostly assuming SSB (voice). Other modes are different. For example, with CW (morse) exchanges will generally be more concise. Then there's more "useful" modes, for example you could send/receive email over Winlink via a digital mode like VARA. This doesn't really benefit from extreme reach, but depending on which bands you have antennas for, the next station might be e.g. a thousand miles away, so this is more of a mid-range thing. In contrast, some digital modes like WSPR focus entirely on propagation research (/ antenna testing), and _automatically_ communicate the callsign, transmit power, location and _nothing else_, but getting (automated) reports from stations on the other side of the globe that have heard your very modestly powered transmissions feels pretty rewarding.
Also note that there are phenomena that give you long range, like grayline DX (good propagation along the day/night line), tropospheric ducting (bounces earth->sky->sky->sky->...->earth) and moonbounce/EME (earth->moon->earth). Trying these is fun in itself even without meaningful information exchanged. There's also ham radio satellites; including one in geostationary orbit (Es'hail 2). If you hit one, you can hit more or less your entire continent. There the fun is using the satellite; the reach is generally a welcome side effect.
First, the ionosphere bounces a lot of radio traffic right back down to the planet, amateur radio operators (like me) use that to talk to stations farther away on planet but it doesn't go into space.
Second the frequencies that do travel through the ionosphere are typically aimed at satellites (geosynchronous or lower) and are scaled to have a level of power that gets there reliably but without an overly large margin for error.
Third, the Sun is a very "noisy" source of RF energy and someone looking this way at us would also be looking at the Sun as well (if you're looking at transits). In terms of radio frequencies that they could perhaps analyze it would require a lot of filtering.
The analysis we've done on transiting planets so far is based on spectroscopy using the star as a huge light source and looking for how that light is filtered by the 'edges' of the planet. (so through the atmosphere of the planet).
If they are doing that, then the change in atmosphere composition over the last 1000 years seems like it would be detectable.