When I turn the wheel all the way to the left and start moving I hear a "clunk"-like noise

A single clunk or a continuous click - click as you start to move?

Time for an inspection at a tire and alignment shop. If the clunk occurs while the car is not moving, the most likely cause is a worn upper strut mount. That is not serious but it can be irritating.

Lower ball joints can clunk too but they will occur more than just when turning as it gets worse. You don't want a ball joint separating because the bottom of that wheel will squirt out and cause a loss of control. It will lead to damage to that half shaft too. Tie rod ends don't typically clunk when turning the steering wheel since there will be lots of pressure on them. Struts and anti-sway bar links and bushings can also clunk but you'll usually hear them over bumpy roads. All of these things will be inspected by the mechanic.