The connections to the CPU are usually by means of 'power planes' rather than simple traces on the motherboard PCB. Essentially, there are 2 copper layers, one for ground and one for power, which are essentially solid copper expect for insulating space around the CPU pins they don't connect to. In fact there are power planes that extend thoughout the whole motherboard routing Ground, 3.3 V and 5V, CPU and memory core voltages to the appropriate parts - although it is possible to have the various power rails divided into large blocks over a single layer).
The power planes (which are actually internal to the motherboard, and therefore not visible from the outside) are also often considerably thicker than the external layers - potentially as thick as 0.35 mm each. The external layers that carry signals need fine wires for space, and the copper needs to be thinner in order to make manufacturing practical.
There are also additional tricks to ensure that the power is stable. Whenever power flows through a wire it causes a voltage drop - try this at home, switch on a heavy load and you'll see the lights dim as voltage is lost in the wires carrying power to your house. There may well be a significant drop in the planes carrying power from the regulator to the chip - and potentially a significant amount lost in the socket and CPU pins. To get around this, there are 2 pins on modern CPUs which are connected directly to the power supply on the die - these pins allow the actual voltage reaching the silicon. The voltage regulator circuit measures this and regulates this to keep it properly regulated. Note that this voltage is not always measured by 'health monitoring' chips, so they will give an inaccurate value for CPU core voltage.
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