Direct imaging (DI) campaigns are uniquely suited to probing the outer regions around young stars and looking for giant exoplanet and brown dwarf companions, hence providing key complementary information to radial velocity (RV) and transit searches for the purpose of demographic studies. However, the critical 5-20 au region, where most giant planets are thought to form, remains poorly explored, lying in-between RV and DI capabilities. Significant gains in detection performances can be attained at no instrumental cost by means of advanced post-processing techniques. In the context of the COBREX project, we have assembled the largest collection of archival DI observations to date in order to undertake a large and uniform re-analysis. In particular, this paper details the re-analysis of 400 stars from the GPIES survey operated at GPI@Gemini South. Following the pre-reduction of raw frames, GPI data cubes were processed by means of the PACO algorithm. Candidates were identified and vetted based on multi-epoch proper motion analysis -- whenever possible -- and by means of a suitable color-magnitude diagram. The conversion of detection limits into detectability maps allowed for an estimate of unbiased occurrence frequencies of giant planets and brown dwarfs. Deeper detection limits were derived compared to the literature, with up to a twofold gain in minimum detectable mass compared to previous GPI-based publications. Although no new substellar companion was confirmed, we identified two interesting planet candidates awaiting follow-up observations. We derive an occurrence rate of $1.7_{-0.7}^{+0.9}\%$ for $5$~\mjup$ < m < 13$~\mjup planets in $10~\text{au}< a < 100~\text{au}$, that raises to $2.2_{-0.8}^{+1.0}\%$ when including substellar objects up to 80 \mjup. Our results are in line with the literature, but come with lower uncertainties thanks to the enhanced detection sensitivity. We confirm the finding, hinted at by previous studies, of a larger occurrence of giant planets around BA hosts compared to FGK stars; moreover, we tentatively observe a smaller occurrence of brown dwarf companions around BA stars, although larger samples are needed to shed light on this point. While waiting for the wealth of data expected from future instrument and facilities, valuable information can still be extracted from existing data. In this regard, a complete re-analysis of SPHERE and GPI data is expected to provide the most precise demographic constraints ever provided by imaging.