Electron correlations in the kagome metals <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mtext>AV</mml:mtext><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mtext>Sb</mml:mtext><mml:mn>5</mml:mn></mml:msub><mml:mo> </m

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 $(U)$ and intersite $(V)$ 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 $d\ensuremath{-}dp$ 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.