We investigate the group-scale environment of 15 luminous quasars (luminosity L$_{3000}$ > 10$^{46}$ erg s$^{−1}$) from the Cosmic Ultraviolet Baryon Survey (CUBS) at redshift z ≈ 1. Using the Multi Unit Spectroscopic Explorer integral field spectrograph on the Very Large Telescope, we conduct a deep galaxy redshift survey in the CUBS quasar fields to identify group members and measure the physical properties of individual galaxies and galaxy groups. We find that the CUBS quasars reside in diverse environments. The majority (11 out of 15) of the CUBS quasars reside in overdense environments with typical halo masses exceeding 10$^{13}$M$_{⊙}$, while the remaining quasars reside in moderate-size galaxy groups. No correlation is observed between overdensity and redshift, black hole (BH) mass, or luminosity. Radio-loud quasars (5 out of 15 CUBS quasars) are more likely to be in overdense environments than their radio-quiet counterparts in the sample, consistent with the mean trends from previous statistical observations and clustering analyses. Nonetheless, we also observe radio-loud quasars in moderate groups and radio-quiet quasars in overdense environments, indicating a large scatter in the connection between radio properties and environment. We find that the most UV luminous quasars might be outliers in the stellar mass-to-halo mass relations or may represent departures from the standard single-epoch BH relations.