KiDS-Legacy: Covariance validation and the unified OneCovariance framework for projected large-scale structure observables

We introduce OneCovariance, an open-source software designed to accurately compute covariance matrices for an arbitrary set of two-point summary statistics across a variety of large-scale structure tracers. Utilising the halo model, we estimated the statistical properties of matter and biased tracer fields, incorporating all Gaussian, non-Gaussian, and super-sample covariance terms. The flexible configuration permits user-specific parameters, such as the complexity of survey geometry, the halo occupation distribution employed to define each galaxy sample, or the form of the real-space and/or Fourier space statistics to be analysed. We illustrate the capabilities of OneCovariance within the context of a cosmic shear analysis of the final data release of the Kilo-Degree Survey (KiDS-Legacy). Upon comparing our estimated covariance with measurements from mock data and calculations from independent software, we ascertain that OneCovariance achieves accuracy at the per cent level. When assessing the impact of ignoring complex survey geometry in the cosmic shear covariance computation, we discover misestimations at approximately the 10% level for cosmic variance terms. Nonetheless, these discrepancies do not significantly affect the KiDS-Legacy recovery of cosmological parameters. We derive the cross-covariance between real-space correlation functions, bandpowers, and COSEBIs, facilitating future consistency tests among these three cosmic shear statistics. Additionally, we calculate the covariance matrix of photometric-spectroscopic galaxy clustering measurements, validating the jackknife covariance estimates for calibrating KiDS-Legacy redshift distributions. The OneCovariance can be found on GitHub (https://github.com/rreischke/OneCovariance) together with comprehensive documentation and examples.