Dark Energy Survey: Galaxy sample for the baryonic acoustic oscillation measurement from the final dataset

In this paper we present and validate the galaxy sample used for the analysis of the baryon acoustic oscillation (BAO) signal in the Dark Energy Survey (DES) Y6 data. The definition is based on a color and redshift-dependent magnitude cut optimized to select galaxies at redshifts higher than 0.6, while ensuring a high-quality photo-$z$ determination. The optimization is performed using a Fisher forecast algorithm, finding the optimal $i$-magnitude cut to be given by $i$<19.64+2.894$z_{\rm ph}$. For the optimal sample, we forecast an increase in precision in the BAO measurement of $\sim$25% with respect to the Y3 analysis. Our BAO sample has a total of 15,937,556 galaxies in the redshift range 0.6<$z_{\rm ph}$<1.2, and its angular mask covers 4,273.42 deg${}^2$ to a depth of $i$=22.5. We validate its redshift distributions with three different methods: directional neighborhood fitting algorithm (DNF), which is our primary photo-$z$ estimation; direct calibration with spectroscopic redshifts from VIPERS; and clustering redshift using SDSS galaxies. The fiducial redshift distribution is a combination of these three techniques performed by modifying the mean and width of the DNF distributions to match those of VIPERS and clustering redshift. In this paper we also describe the methodology used to mitigate the effect of observational systematics, which is analogous to the one used in the Y3 analysis. This paper is one of the two dedicated to the analysis of the BAO signal in DES Y6. In its companion paper, we present the angular diameter distance constraints obtained through the fitting to the BAO scale.