How do bypass capacitors recharge in high-frequency if the PCB can't deliver high-frequency currents?
Consider a simple LC model of the power network wherein a time dependent current source represents the IC current drawn from the bypass capacitor \$C\$ with \$L\$ being the power plane inductance to the capacitor.







simulate this circuit &ndash; Schematic created using CircuitLab

As the high frequency current \$i(t)\$ is drawn the capacitor will discharge. However, the power supply will then charge the capacitor through the inductor \$L\$. The inductance prevents the current from changing rapidly, so the capacitor's voltage will drop a certain amount. Eventually the inductor current will increase enough to start charging the capacitor. Although \$i(t)\$ is discharging the capacitor at high frequency, as long as the average current through the inductor is larger, the capacitor will charge.

The capacitor voltage will not be completely stable. It will drop when \$i(t)\$ is large, but as \$i(t)\$ decreases the inductor current will charge it back to its maximum value. So you get a small oscillation at the bypass capacitor. However, as long as the voltage does not drop below the operating range of the IC that won't be a problem.