Does the Cosmological Constant really indicate the existence of a Dark Dimension?

According to the “dark dimension” (DD) scenario, we might live in a universe with a single compact extra dimension, whose mesoscopic size is dictated by the measured value of the cosmological constant. This scenario is based on swampland conjectures, that lead to the relation ${\rho }_{\mathrm{s}\mathrm{w}\mathrm{a}\mathrm{m}\mathrm{p}}\sim m_{{}_{\mathrm{K}\mathrm{K}}}^4$ between the vacuum energy ${\rho }_{\mathrm{s}\mathrm{w}\mathrm{a}\mathrm{m}\mathrm{p}}$ and the size of the extra dimension $m_{{}_{\mathrm{K}\mathrm{K}}}^{-1}$ ($m_{{}_{\mathrm{K}\mathrm{K}}}$ is the mass scale of a Kaluza-Klein tower), and on the corresponding result ${\rho }_{{}_{\mathrm{E}\mathrm{F}\mathrm{T}}}$ from the EFT limit. We show that ${\rho }_{{}_{\mathrm{E}\mathrm{F}\mathrm{T}}}$ contains previously missed UV-sensitive terms, whose presence invalidates the widely spread belief (based on existing literature) that the calculation gives automatically the finite result ${\rho }_{{}_{\mathrm{E}\mathrm{F}\mathrm{T}}}\sim m_{{}_{\mathrm{K}\mathrm{K}}}^4$ (with no need for fine-tuning). This renders the matching between ${\rho }_{\mathrm{s}\mathrm{w}\mathrm{a}\mathrm{m}\mathrm{p}}$ and ${\rho }_{{}_{\mathrm{E}\mathrm{F}\mathrm{T}}}$ a non-trivial issue. We then comment on the necessity to find a mechanism that implements the suppression of the aforementioned UV-sensitive terms. This should finally allow to frame the DD scenario in a self-consistent framework, also in view of its several phenomenological applications based on EFT calculations.