2013-2021 models have a single gear-CVT which makes a droning sound in normal mode as you speed up, and typically goes away once you settle into a specific speed. Sport mode adds multiple small pauses to simulate shift points as you speed up. Unfortunately, it doesn't make the acceleration more agressive or change the suspension, but does make it feel like a regular car starting up.
If the klunky feeling is new, then you should consider getting it checked out next time you're in for repairs.
FYI, if cruise control speed-up is too aggressive/jurky, try ECO (while in CC only) since it'll also smooth out the drive.