  We investigate the interior of a dynamical black hole as described by the
Einstein-Maxwell-charged-Klein-Gordon system of equations with a cosmological
constant, under spherical symmetry. In particular, we consider a characteristic
initial value problem where, on the outgoing initial hypersurface, interpreted
as the event horizon $\mathcal{H}^+$ of a dynamical black hole, we prescribe:
a) initial data asymptotically approaching a fixed sub-extremal
Reissner-Nordstr\"om-de Sitter solution; b) an exponential Price law upper
bound for the charged scalar field. After showing local well-posedness for the
corresponding first-order system of partial differential equations, we
establish the existence of a Cauchy horizon $\mathcal{CH}^+$ for the evolved
spacetime, extending the bootstrap methods used in the case $\Lambda = 0$ by
Van de Moortel. In this context, we show the existence of $C^0$ spacetime
extensions beyond $\mathcal{CH}^+$. Moreover, if the scalar field decays at a
sufficiently fast rate along $\mathcal{H}^+$, we show that the renormalized
Hawking mass remains bounded for a large set of initial data. With respect to
the analogous model concerning an uncharged and massless scalar field, we are
able to extend the known range of parameters for which mass inflation is
prevented, up to the optimal threshold suggested by the linear analyses by
Costa-Franzen and Hintz-Vasy. In this no-mass-inflation scenario, which
includes near-extremal solutions, we further prove that the spacetime can be
extended across the Cauchy horizon with continuous metric, Christoffel symbols
in $L^2_{\text{loc}}$ and scalar field in $H^1_{\text{loc}}$. By generalizing
the work by Costa-Gir\~ao-Nat\'ario-Silva to the case of a charged and massive
scalar field, our results reveal a potential failure of the
Christodoulou-Chru\'sciel version of the strong cosmic censorship under
spherical symmetry.
