Studying the composition and origin of the inner region of our Galaxy—the "Galactic bulge"—is crucial for understanding the formation and evolution of the Milky Way and other galaxies. We present new observational constraints based on a sample of around 18 000 stars in the inner Galaxy, combining Gaia DR3 RVS and APOGEE DR17 spectroscopy. Gaia-RVS complements APOGEE by improving the sampling of the metallicity, [Fe/H], in the −2.0 to −0.5 dex range. This work marks the first application of Gaia-RVS spectroscopy to the bulge region, enabled by a novel machine learning approach (hybrid-CNN) that derives stellar parameters from intermediate-resolution spectra with precision comparable to APOGEE's infrared data. We performed full orbit integrations using a barred Galactic potential and applied orbital frequency analysis to disentangle the stellar populations in the inner Milky Way. For the first time, we are able to robustly identify the long-sought pressure-supported bulge traced by the field stars. We show this stellar population to be chemically and kinematically distinct from the other main components co-existing in the same region. The spheroidal bulge has a metallicity distribution function (MDF) peak at around −0.70 dex extending to solar values. It is dominated by a high-[α∕Fe] population with almost no dependency on metallicity, consistent with very rapid early formation predating the thick disc and the bar. We find evidence that the bar has influenced the dynamics of the spheroidal bulge, introducing a mild triaxiality and radial extension. We identify a group of stars on X4 orbits, likely native to the early spheroid, as this population mimics the chemistry of the spheroidal bulge, with a minor contamination from the more metal-poor ([Fe∕H]< −1.0) halo. We find the inner thick disc to be kinematically hotter (Vφ ≍ 125 km s−1) than the local thick disc. The disc, chemically distinct from the spheroidal bulge and bar, is predominantly metal-poor with an MDF peak at [Fe/H] ≍ −0.45 dex and includes a high fraction of stars with sub-solar [Fe/H] and intermediate [α/Fe]. In contrast to the spheroidal bulge, the [α/Fe] disc shows a steeper decline with [Fe/H], consistent with smaller star formation efficiency than that of the spheroidal bulge. Both the thick disc and the spheroidal bulge present vertical metallicity gradients. We find that the Galactic bar contains both metal-rich and metal-poor stars, as well as high and low [α/Fe] in nearly equal measure. However, their relative contributions vary significantly across different orbital families. The bar shows no strong metallicity trends in orbital extent or velocity dispersions and maintains a consistent elongated shape across all metallicities, indicating that it is a well-mixed dynamical structure. Despite their spatial overlap, the spheroidal bulge, thick disc, and bar occupy distinct regions in both phase space and chemical abundance, indicating separate formation pathways. The stars with [Fe/H]< −1.0 and crossing the Galactic bulge are comprised by accreted populations primarily (70%) belonging to the Gaia-Enceladus/Sausage (GES) merger with an MDF peak at −1.30 dex and possibly a secondary merger remnant with an MDF peak at −1.80 dex.