  We analyse spectroscopic and photometric transits of the hot Jupiters
WASP-52b and HAT-P30b obtained with ESPRESSO, Eulercam and NGTS for both
targets, and additional TESS data for HAT-P-30. Our goal is to update the
system parameters and refine our knowledge of the host star surfaces. For
WASP-52, the companion planet has occulted starspots in the past, and as such
our aim was to use the reloaded Rossiter-McLaughlin technique to directly probe
its starspot properties. Unfortunately, we find no evidence for starspot
occultations in the datasets herein. Additionally, we searched for stellar
surface differential rotation (DR) and any centre-to-limb variation (CLV) due
to convection, but return a null detection of both. This is unsurprising for
WASP-52, given its relatively cool temperature, high magnetic activity (which
leads to lower CLV), and projected obliquity near 0 degrees (meaning the
transit chord is less likely to cross several stellar latitudes). For HAT-P-30,
this result was more surprising given its hotter effective temperature, lower
magnetic field, and high projected obliquity (near 70 degrees). To explore the
reasons behind the null DR and CLV detection for HAT-P-30, we simulated a
variety of scenarios. We find that either the CLV present on HAT-P-30 is below
the solar level or the presence of DR prevents a CLV detection given the
precision of the data herein. A careful treatment of both DR and CLV is
required, especially for systems with high impact factors, due to potential
degeneracies between the two. Future observations and/or a sophisticated
treatment of the red noise present in the data (likely due to granulation) is
required to refine the DR and CLV for these particular systems; such
observations would also present another opportunity to try to examine starspots
on WASP-52.
