  We study Type IIB supergravity solutions with spacetime of the form
$AdS_6\times S^2$ warped over a Riemann surface $\Sigma$, where $\Sigma$
includes punctures around which the supergravity fields have non-trivial
$SL(2,R)$ monodromy. Solutions without monodromy have a compelling
interpretation as near-horizon limits of $(p,q)$ 5-brane webs, and the
punctures have been interpreted as additional 7-branes in the web. In this work
we provide further support for this interpretation and clarify several aspects
of the identification of the supergravity solutions with brane webs. To further
support the identification of the punctures with 7-branes, we show that
punctures with infinitesimal monodromy match a probe 7-brane analysis using
$\kappa$-symmetry. We then construct families of solutions with fixed 5-brane
charges and punctures with finite monodromy, corresponding to fully backreacted
7-branes. We compute the sphere partition functions of the dual 5d SCFTs and
use the results to discuss concrete brane web interpretations of the
supergravity solutions.
