The investigation of electronic order-quantum phase interplay in kagome lattices commonly employs the extended kagome-Hubbard model, where the critical parameters comprise on-site $\left(U\right)$ and intersite $\left(V\right)$ Coulomb interactions. In prototypical kagome metals ${\mathrm{AV}}_3{\mathrm{Sb}}_5 (\mathrm{A}=\mathrm{K}, \mathrm{Rb}, \mathrm{Cs})$, the geometrically frustrated quasi-two-dimensional architecture induces pressure-dependent complexity in vanadium $d$-electron correlations, necessitating systematic theoretical scrutiny. Utilizing the $d-dp$ model within constrained random phase approximation (cRPA), we quantified $U$, $V$, and Hund's coupling $J$ under hydrostatic pressure (0–9 GPa). While ${\mathrm{KV}}_3{\mathrm{Sb}}_5$ and ${\mathrm{RbV}}_3{\mathrm{Sb}}_5$ exhibit pressure-insensitive interaction parameters, ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ manifests anomalous discontinuities in $U$ and $V$ near 0.2 GPa, suggesting a first-order electronic phase transition. This work establishes cRPA-derived interaction landscapes as critical predictors for pressure-tunable quantum phenomena in correlated kagome systems, offering insight into the understanding of the interplay between the charge density wave transition and the double superconductivity dome in ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ at low pressure.

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• Charge density waves
• Superconductivity
• Kagome metal
• Strongly correlated systems
• First-principles calculations
• Random phase approximation