I want to prove that weak descent of a $1$-category implies the classical Giraud axioms.

More precisely, let $\mathsf{C}$ be a cocomplete, finitely complete $1$-category. We say that $\mathsf{C}$ satisfies weak descent if the following conditions are satisfied:

• $(\mathbf{D1}a)$-(Universal coproducts): Given a collection of objects $\{ Y_i \}_{i \in I}$, let $Y = \coprod_i Y_i$. Let $f: X \to Y$ be a morphism, and let $X_i = Y_i \times_Y X$. Then the induced map $\coprod_i X_i \to X$ is an isomorphism,
• $(\mathbf{D1}b)$-(Universal pushouts): Given a span $Y_0 \leftarrow Y_1 \to Y_2$, let $Y = Y_0 \coprod_{Y_1} Y_2$. Let $f: X \to Y$ be a morphism and let $X_i = Y_i \times_{Y} X$. Then the induced map $X_0 \coprod_{X_1} X_2 \to X$ is an isomorphism.
• $(\mathbf{D2}a)$-(Effective coproducts): Given a collection of maps $\{ f_i: X_i \to Y_i \}$, let $X = \coprod_i X_i$, and $Y = \coprod_i Y_i$, and let $f: X \to Y$ be the coproduct $\coprod_i f_i$. Then the natural maps $X_i \to Y_i \times_Y X$ are isomorphisms for each $i$.
• $(\mathbf{D2}b)$-(Weak effective pushouts): Given a map of spans: $\require{AMScd}$ \begin{CD} X_0 @<<< X_1 @>>> X_2\\ @Vf_0VV @Vf_1VV @Vf_2VV\\ Y_0 @<<< Y_1 @>>> Y_2 \end{CD} let $X = X_0 \coprod_{X_1} X_2$ and $Y = Y_0 \coprod_{Y_1} Y_2$, and let $f:X \to Y$ denote the induced map of pushouts. Then the natural maps $X_i \to Y_i \times_Y X$ are regular epimorphisms.

Condition $(\mathbf{D2}b)$ is the real difference between $1$-topoi and $\infty$-topoi, and I am trying to better understand this comparison. Now recall the classical Giraud Axioms:

• $(\mathbf{G1})$ Coproducts are disjoint, namely $A \times_{A \coprod B} B \cong \varnothing$,
• $(\mathbf{G2})$ For any morphism $f: X \to Y$, the base change functor $f^*: \mathsf{C}_{/Y} \to \mathsf{C}_{/X}$ preserves colimits,
• $(\mathbf{G3})$ Equivalence relations are effective.

Rezk sketches how to prove that $(\mathbf{D1}) = (\mathbf{D1}a) \wedge (\mathbf{D1}b)$ is equivalent to $(\mathbf{G2})$, and that $(\mathbf{D2}a) \implies (\mathbf{G1})$.

My suspicion is that $(\mathbf{D2}b) \implies (\mathbf{G3})$ or is possibly equivalent to it, but I can't quite see how to prove it. I also suspect that the way one can prove it by is proving that $(\mathbf{D2}b)$ is equivalent to the coequalizer defining equivalence relations being effective. Namely if $R \xrightarrow{(s,t)} X \times X$ is an equivalence relation, then $R \rightrightarrows X \to X/R$ is a coequalizer iff $X/R \cong R \coprod_{R \coprod R} X$, and my idea is to show that having condition $(\mathbf{D2}b)$ hold, but this time up to isomorphism rather than regular epi but only for pushouts of equivalence relations as above, and this would be equivalent to $(\mathbf{D2}b)$ and from this somehow it would be easier to see that it implies $(\mathbf{G3})$, but I've had no luck with this either.

Any ideas or insight would be appreciated.