Searching for GEMS: Two Super-Jupiters around M-dwarfs -- Signatures of Instability or Accretion?

We present the discovery of TOI-6303b and TOI-6330b, two massive transiting super-Jupiters orbiting a M0 and a M2 star respectively, as part of the Searching for GEMS survey. These were detected by TESS and then confirmed via ground-based photometry and radial velocity observations with the Habitable-zone Planet Finder (HPF). TOI-6303b has a mass of 7.84 +/- 0.31 MJ, a radius of 1.03 +/- 0.06 RJ , and an orbital period of 9.485 days. TOI-6330b has a mass of 10.00 +/- 0.31 MJ , a radius of 0.97 +/- 0.03 RJ , and an orbital period of 6.850 days. We put these planets in context of super-Jupiters around M-dwarfs discovered from radial-velocity surveys, as well as recent discoveries from astrometry. These planets have masses that can be attributed to two dominant planet formation mechanisms - gravitational instability and core-accretion. Their masses necessitate massive protoplanetary disks that should either be gravitationally unstable, i.e. forming through gravitational instability, or be amongst some of the most massive protoplanetary disks to form objects through core-accretion. We also discuss the eccentricity distribution of these objects, as a potential indicator of their formation and evolutionary mechanisms.