Proving heat and enthalpy equivalence for an isobaric process

We can prove that enthalpy is equivalent to the heat $q$ for constant pressure process by the following derivation:

$$ d H = dU + d (PV)$$

Or,

$$ d H = d q – P_{ext} dV + P d V$$

Now, this is the step that is bugging me.. in websites which I’ve seen, they cancel of $ -P_{ext} Delta V $ and $ P Delta V$ term but the external pressure is only equal to internal pressure at equilibrium (*).

So, does the equivalent of heat being equal to pressure only apply for a reversible isobaric process?

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(*): In the definition section of Wikipedia, the write that the pressure term in the $d(PV)$ term is the pressure of the system (see here)