After thousands of years, what will be left of us?
It will be fairly evident that an advanced species lived here. The ring of satellites in the geostationary belt will be quick evidence of that. Even after millennia, those will only have drifted so far, and they're an obvious thing to look for. Lower satellites will be long gone, no Hubble or ISS, probably even the GPS constellation will be gone, but all the comms sats in geostationary orbit will be more or less still there.
Nuclear waste would be another obvious sign. Those isotopes aren't natural, and some of them last millions of years. And we're deliberately putting them in places where they'll be stable and unmolested. It's not that easy to find, but if they do stumble across it, it's an unambiguous sign. And with relatively simple instruments, they could probably pick up the fallout of nuclear weapons, though I'm not 100% sure they'd still be recognizably artificial by that point.
Plastics are also pretty long-lasting. Not quite as bad as some fear, but still easy to stumble over, and pretty clearly artificial. Some ceramics are also likely to last that long - our sewage infrastructure is built to last, because nobody wants to be the one replacing it.
If it's only a few millennia, there's likely to be some ruins. The great dams aren't going to still be standing, but the remnants will be there. The open-pit mines will not have been filled in. Some of the larger metal works might remain - heavy iron engine blocks will take a very long time to rust, especially those in the desert. Look at artificial reefs made by sinking battleships and tanks and other military hardware - literally immersed in saltwater, still haven't corroded away. Those will be gone within a few centuries, probably, but stuff like the Arizona Aircraft Boneyard will last quite a lot longer, at least in pieces.
After thousands of years, I'm not sure what exactly will remain of our records, our writing and media. It takes some very special conditions for those to last a thousand years... but on the other hand, we do have a LOT of it, and we've got piles of ten-thousand-year-old Mesopotamian and Egyptian writing. 0.001% times an unfathomably large number is still a LOT. So if the aliens realize there was an intelligent species here, and start some serious archeology, they'll probably find a lot.
What they'll mostly find, judging from our own archeology, is fairly boring stuff. A lot of accounting ledgers, a lot of tax paperwork, a lot of boring legal documents. Probably a fair few religious texts - with a billion bibles printed, surely some will be among the survivors - but everything else will be a crapshoot. I would not expect them to have that great an understanding of our actual daily lives, or to recover a lot of our fiction in useful form. (Consider: Ancient Greece was only a few thousand years ago, and our culture directly descends from them, but we've lost the majority of their dramas and comedies. With zero effort ongoing to preserve them, our own media will likely fare even worse.)
The wild card is going to be digital media. On the one hand, some of it's incredibly fragile, was never built to last even a decade, let alone a thousand decades. But on the other hand, we have a ton of data centers built in bomb shelters, deep underground, in highly-stable environments, and we have just SO. MUCH. that surely something must survive. And if so... it's about 50% logs that even us humans never read, 40% porn of one flavor or another, and 10% everything else. (The archeological propensity for discovering "artifacts that likely played a role in fertility rituals" seems apt to mention at this point.)
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