Discovery of a pair of very metal-poor stars enriched in neutron-capture elements: The proto-disk r-II star BPS CS 29529-0089 and the Gaia-Sausage-Enceladus r-I star TYC 9219-2422-1

R-process enhanced metal-poor stars (\EuFe$\geq+0.3$ and \FeH$\leq-1.0$) are rare objects whose study can provide clues to the astrophysical sites of the rapid neutron capture process. In this study, we investigate the detailed chemical abundance patterns of two of these anomalous stars, originally identified among stars observed by the GALAH survey. Our aim is to obtain the detailed chemical abundance pattern of these stars with spectroscopy at higher resolution and signal-to-noise ratio. We use a calibration of the infrared flux method to determine accurate effective temperatures, and \Gaia~ parallaxes together with broadband photometry and theoretical bolometric corrections to determine surface gravity. Metallicities and chemical abundances are determined with model atmospheres and spectrum synthesis. We also integrate stellar orbits for a complete chemodynamic analysis. e determine abundances for up to 47 chemical species (44 elements), of which 27 are neutron-capture elements. Corrections because of deviations from the local thermodynamical equilibrium are applied to the metallicities and 12 elements. We find that one of the stars, BPS CS 29529-0089, is a proto-disk star of the Milky Way of r-II type, with \EuFe=+1.79~dex. The second star, TYC 9219-2422-1, is part of the halo and associated with the Gaia-Sausage-Enceladus merger event. It is of r-I type with [Eu/Fe] = +0.54. Abundances of Th are also provided for both stars. BPS CS 29529-0089 is the most extreme example of r-process enhanced star known with disk-like kinematics and that is not carbon enhanced. TYC 9219-2422-1 is found to be an archetypal Gaia-Sausage-Enceladus star. Their abundances of C, Mg, Ni, Sc, Mn, and Al seem consistent with expectations for stars enriched by a single population III core collapse supernova, despite their relatively high metallicities ([Fe/H] $\sim$ $-$2.4).