Blind mitigation of foreground-induced biases on primordial $B$ modes for ground-based CMB experiments

Observations of the Cosmic Microwave Background (CMB) B-mode polarisation provide a unique probe of inflationary physics. Extracting a reliable constraint on the tensor-to-scalar ratio $r$ nonetheless demands stringent suppression of diffuse Galactic foregrounds, whose residuals can bias the inferred signal. This work introduces and evaluates two extensions of the Needlet Internal Linear Combination (NILC) framework aimed at reducing foreground-induced biases on $r$. The first extension implements the deprojection of selected foreground moments directly within the component-separation step. The second performs a likelihood-level marginalisation over residual foreground power using a data-driven template. Using Simons Observatory Small Aperture Telescope (SO-SAT) - like simulations, we show that both methods effectively control residual contamination, yielding unbiased estimates of $r$ and a consistent reconstruction of the lensing B-mode amplitude. These results indicate that enhanced foreground-mitigation strategies will be useful for next-generation CMB polarisation analyses seeking a robust detection of primordial B-modes.