De Broglie relations use which frequency or frequencies of a wave packet? The Wikipedia article about matter waves lists the De Broglie relation for the frequency $f$ of a matter wave as
$$ E = hf = \hbar\omega $$
with Planck constant $h$, total energy $E$ and angular frequency $\omega$.
The article also explains phase and group velocity of the matter wave being different, so the matter wave is rather a wave packet i.e. a sum or integral of waves each having their own frequency and wave length. Approximately we can have
$$\omega(k) = \omega_0 + v_g(k - k_0)$$
as a relation between the $\omega$s of the individual waves of the wave packet and their wave vector $k$ with $v_g$ being the group velocity and $k_0$ and $\omega_0$ some constant values.
Question: Which of the $\omega(k)$ or $\omega_0$ or some combination of them appears in the De Broglie relation $E = \hbar\omega$?
 A: The answer to your question is that the frequency that appears in the De Broglie relations is the function $\omega(k)$. Note that the Wikipedia article on group velocity that you quote says:

If the wavepacket has a relatively large frequency spread, or if the dispersion ω(k) has sharp variations (such as due to a resonance), or if the packet travels over very long distances, this assumption is not valid, and higher-order terms in the Taylor expansion become important.

In the context of matter waves, this linear approximation of the frequency as a function of wavenumber does not hold (why?) and one can actually derive a dispersion relation that is valid for matter waves. Remember that not only the relation $E=\hbar \omega$ holds, but also $p=\hbar k$, and as we know from classical mechanics, $E=\frac{p^2}{2m}$ (for a free particle). So substituting the equations for $E$ and $p$ in terms of $\omega$ and $k$ respectively, we arrive at the dispersion relation $\omega(k)=\frac{\hbar k²}{2m}$. I leave as an exersice to the OP the job of calculating and interpreting what the derivative of this expression for $\omega$ with respect to $k$.
