In ideal circuit theory, KVL holds period.
Consider the series RLC circuit driven by an arbitrary voltage source $v_s$. The canonical differential equation for the series current $i(t)$ is:
$$\dfrac{d^2i}{dt^2} + \dfrac{R}{L}\dfrac{di}{dt} + \dfrac{1}{LC}i = \dfrac{1}{L}\dfrac{dv_s}{dt}$$
Where does this equation come from? It comes from writing the KVL equation around the loop in terms of the series current $i$:
$$v_s(t) = Ri(t) + L\dfrac{di(t)}{dt} + \dfrac{1}{C}\int_{-\infty}^ti(\tau)d\tau$$
Now, it is true that if the assumptions of ideal circuit theory do not hold, KVL does not hold. However, understand that AC circuit analysis is under the umbrella of ideal circuit theory thus, in that context, KCL holds for AC circuit analysis.
In response to a comment:
Then say for example, the current in a circuit with resistance and a
capacitance is $I$. then $V_R=IR$ and $V_C=I/ωC$. But the supply voltage
$V=\sqrt{V^2_R+V^2_C}$ and not $V=V_R+V_C$. Does this not violate KVL?
First, the phasor voltage across the capacitor is $\vec V_c = \dfrac{1}{j \omega C}\vec I$. Phasors are complex numbers. The sum of magnitudes is generally not equal to the magnitude of the sum:
$$|Z_1| + |Z_2| \ne |Z_1 + Z_2|$$
Thus, the sum of resistor and capacitor phasor voltage magnitudes is not meaningful but the sum of the resistor and capacitor phasor voltages is.
Let $v_1(t) = V_1 \sin \omega t$ and $v_2(t) = V_2 \cos \omega t$ be the time domain voltages across two series circuit elements. By KVL, the voltage across the series combination is
$$v_s(t) = v_1(t) + v_2(t) = V_1\sin \omega t + V_2 \cos \omega t = \sqrt{V^2_1 + V^2_2}\cos(\omega t - \phi)$$
where
$$\tan\phi = \frac{V_1}{V_2}$$
Note that, using phasors, the above is
$$\vec V_s = \vec V_1 + \vec V_1 = -jV_1 + V_2 = e^{-j \phi}\sqrt{V^2_1 + V^2_2}$$
Thus, the sum of the phasor magnitudes, $V_1 + V_2$, is not meaningful and certainly isn't an application of KVL.
