gr8stars II : judgement day for spectroscopic parameter model systematics

Many areas of astrophysics, including exoplanetary studies, rely on precise and accurate stellar parameters. This demands that uncertainties on these parameters truly reflect all biases and systematics. Within this second work of the \texttt{gr8stars} collaboration, we take a set of 585 bright FGK dwarfs with high resolution, high signal-to-noise ratio spectra from the SOPHIE spectrograph. We determine stellar effective temperature, surface gravity, and metallicity using five different spectroscopic methods for each star, with an additional method used for comparisons. We find a typical scatter of 76 K in \teff, 0.14 dex in \logg, and 0.07 dex in \feh. These deviations are significantly larger than the average precision error on these parameters. We furthermore use isochrone fitting to determine mass, radius, and age for all 585 stars, using input from all results. We use the radii determined by SED fitting in the first \texttt{gr8stars} paper as a comparison to our isochronal radii from this work, in addition to comparing the isochronal \logg to spectroscopic \logg. The scatter in mass and radius from the use of different spectroscopic methods is investigated and propagated to exoplanetary parameters. The induced fractional uncertainties in planetary radius ($\lesssim$ 3 \%) and mass ($\lesssim$ 5\%) are found to be below those typically found in the literature. We estimate a lower limit on planetary equilibrium temperature fractional uncertainty of $\approx$ 4\%, a noise floor that is currently not sufficiently represented in the literature.