Achieving and quantifying ultrastrong magnon-magnon coupling (USC) remains a key challenge for quantum magnonics. Here, we demonstrate widely tunable USC between chiral (right- and left-handed) and acoustic or optical magnon modes in the van der Waals antiferromagnet CrPS₄. Using a full quantum model, we decompose the interaction into three microscopic interaction channels: the co-rotating term g₁ (mode hybridization), the counter-rotating term g₂ (two-mode squeezing), and, uniquely in the chiral regime, the self-squared term g₃ that mediates single-mode squeezing. The normalized coupling ratio reaches g/f_g ∼ 0.41, entering the USC regime. Most significantly, we establish a complete protocol linking these USC parameters to a measurable quantum phenomenon: a squeezed magnon vacuum state. Our simulations not only visualize the chirality and polarization evolution of the hybrid modes but also demonstrate how to directly extract quadrature fluctuations and a substantial squeezing factor (up to ∼ 9.7 dB) from thermal noise-driven magnetization dynamics. This work provides a material-specific quantum framework for USC and a practical pathway to detect and exploit non-classical magnon states in low-damping two-dimensional magnets, opening a route toward quantum-enhanced spintronics and hybrid quantum information platforms.