I suppose that when we have a tradeoff between longevity and literally any other useful feature of an artifact, we generally sacrifice longevity; at a 3% annual discount rate, if you can make a durable good last forever instead of 40 years, the extra NPV is only about 44% (or lower if the scrap value is nonzero), and for a substantial number of things we use an even higher discount rate than 3%. Even so, the remains of our civilization would be impossible to avoid seeing for many millennia if it collapsed. Numerous recognizable artifacts would survive for hundreds of millions of years if humanity died today.
I mentioned that the Burj Khalifa will be gone in a century or two; because it's built in a place with corrosive groundwater, it relies on cathodic protection to prevent corrosion in its foundations, and even its above-ground structure will spall due to the corrosion of the steel frame in a few decades, but the crumbled chunks of concrete will remain visibly artificial for hundreds of millions of years. Similarly no lathes and almost no papyri have survived from Khufu's time, but lathes clearly date back at least to Old Kingdom Egypt, before hieroglyphics, because we have the turned stone vessels they made.
What would be left of our own vimanas 4500 years from now if they are left out to weather? The steel parts will surely be just rust. I suspect that the aluminum and titanium parts, if not "looted" by "treasure hunters", will survive for that period of time with only a logarithmically thicker layer of hard protective oxide. The inconel superalloys of the jet engine gas turbines will not weather, though some lesser stainless steels will cease to be so stainless over such a timespan.
The polymers vary widely: cellulose acetate and most of the elastomers are inherently unstable and will degrade into a nasty goo in only a few decades, while PTFE (teflon), polyimide (kapton), polyethylene, polypropylene, and I think PVDF (kynar) are stable over geological timescales. Other organic polymers are in between; in particular I think the glass-fiber-reinforced epoxy circuit boards will last millennia without difficulty, and though the phenol-formaldehyde thermoset used for single-sided circuit boards is also a thermoset, I suspect it might only last a few centuries. PVC has to be mixed with stabilizers to avoid spontaneous degradation in a matter of years, and I don't know how long those stabilizers will last. Surely the naugahyde business-class seat cushions and the polyurethane seat cushions will become as brittle as a mummy; perhaps they will crumble into dust even without disturbance.
Also stable over geological timescales are the glass in the instrument panel and the hair-fine copper wires of the wiring harness, though those, too, will tend to attract treasure hunters. The silicon chips may not still be operable 4500 years from now (due to Flash decay, dopant diffusion, and tin whiskers) but the microscopic patterns on their surfaces will remain, protected by a thick layer of amorphous quartz. The harsh acids today's treasure hunters use to remove their gold bond wires leave the passivated silicon unharmed.
In the playground of my elementary school, I collected thousands of shards of the painted pots from the lost civilization of the Anasazi. They bore abundant silent witness to the perfection enjoyed by the art of pottery in that ancient civilization before its collapse, even devoid of the ephemeral leavings of soups and seeds they once held, and of course lacking any writing. Many of the timbers of the Anasazi survive aboveground, but few places are dry enough to permit that; but the carpentry Eythra 1 well from 7000 years ago, before the Copper Age, was found to have wedged tenons: https://journals.plos.org/plosone/article?id=10.1371/journal...
So I feel safe in asserting that neither the Anasazi nor Khufu's subjects nor the heroes of the Mahabharata knew any art capable of building vimanas. I'm less sure of the settlements predating Jericho and Çatalhöyük: today most of them are under tens of meters of water, and Atlit-Yam seems to have escaped notice for thousands of years despite being in the harbor of Haifa, right in the cradle of civilization. The Antikythera Mechanism survived in a recognizable, if not operable, form, despite two millennia of brine; how many other such paragons of the mechanical art have been lost?