Context. Accurate determination of the chemical abundances in stars plays a pivotal role in understanding stellar structure and evolution, nucleosynthesis, and the chemical enrichment history of the Milky Way. Benchmark stars with precise and accurate atmospheric parameters and abundances are indispensable for calibrating spectroscopic surveys and testing stellar atmosphere models. Aims. This study focuses on the compilation of high-quality spectra and the determination of chemical abundances of iron-peak and α elements for the third version of the Gaia FGK benchmark stars (GBSv3). Methods. We compiled spectra of the GBSv3 from public archives and complemented these with our observations. We used fundamental atmospheric parameters to perform a spectroscopic analysis using the public code iSpec and derived the chemical abundances. Results. We compiled a homogeneous spectral library of high-resolution (42 000) and high signal-to-noise (>100) normalised spectra for 202 stars, including the 192 GBSv3, nine stars with indirect measurement of the angular diameter from previous Gaia FGK benchmark versions, and the Sun. Using four radiative transfer codes, we derived chemical abundances of 13 chemical species (Fe I, Fe II, Mg I, Si I, Ca I, Ti I, Ti II, Sc II, V I, Cr I, Mn I, Co I, Ni I). We performed an in-depth study of several sources of error. Conclusions. The GBSv3 contributes to the legacy samples of spectroscopic reference stars through improved statistics and homogeneity. This work offers the community a homogeneous spectral library and robust reference abundances for iron-peak and α elements, supported by an extensive analysis of the associated uncertainties.