The problem is as follows: when driving in stop and go traffic, at some point I can feel some slight (most passengers are not able to feel them) vibrations in the cabin, accompanied by a "scratchy" feeling in the gas pedal (like scratching something made of metal I believe - the frequency of this is about 1 scratch/second) and a feeling of "something rotating" (I suppose it's synced with the engine's rpm) when I press the clutch pedal. All these symptoms seem to diminish gradually after exiting the stop and go traffic (could also be diminishing because of the start/stop system - they become lower in intensity after the engine gets restarted this way). Stopping the engine for at least an hour seems to completely eliminate these symptoms.
Another possibly useful observation is that going high rpm (like 2500-3500 - when in stop and go traffic) in first or second gear seems to increase the strange feeling in the clutch pedal.
Also, possibly unrelated, when going up a steep hill that has a straight portion in the middle of it, after the front wheels get on the mentioned portion, there starts a more visible vibration in the cabin, which can be mitigated by increasing the engine's rpm (for example, the vibration starts at about 1500 rpm and I accelerate to about 2000 rpm in first gear).
What could be the cause(s) of the specified symptoms? The car I'm talking about is an Audi A3 Limousine from 2015 (2.0 TDI - 150hp; manual transmission - 6 gears; ~160.000 km).
Thank you in advance!