  We compare the observed turbulent pressure in molecular gas,
$P_\mathrm{turb}$, to the required pressure for the interstellar gas to stay in
equilibrium in the gravitational potential of a galaxy, $P_\mathrm{DE}$. To do
this, we combine arcsecond resolution CO data from PHANGS-ALMA with
multi-wavelength data that traces the atomic gas, stellar structure, and star
formation rate (SFR) for 28 nearby star-forming galaxies. We find that
$P_\mathrm{turb}$ correlates with, but almost always exceeds the estimated
$P_\mathrm{DE}$ on kiloparsec scales. This indicates that the molecular gas is
over-pressurized relative to the large-scale environment. We show that this
over-pressurization can be explained by the clumpy nature of molecular gas; a
revised estimate of $P_\mathrm{DE}$ on cloud scales, which accounts for
molecular gas self-gravity, external gravity, and ambient pressure, agrees well
with the observed $P_\mathrm{turb}$ in galaxy disks. We also find that
molecular gas with cloud-scale
${P_\mathrm{turb}}\approx{P_\mathrm{DE}}\gtrsim{10^5\,k_\mathrm{B}\,\mathrm{K\,cm^{-3}}}$
in our sample is more likely to be self-gravitating, whereas gas at lower
pressure appears more influenced by ambient pressure and/or external gravity.
Furthermore, we show that the ratio between $P_\mathrm{turb}$ and the observed
SFR surface density, $\Sigma_\mathrm{SFR}$, is compatible with stellar
feedback-driven momentum injection in most cases, while a subset of the regions
may show evidence of turbulence driven by additional sources. The correlation
between $\Sigma_\mathrm{SFR}$ and kpc-scale $P_\mathrm{DE}$ in galaxy disks is
consistent with the expectation from self-regulated star formation models.
Finally, we confirm the empirical correlation between molecular-to-atomic gas
ratio and kpc-scale $P_\mathrm{DE}$ reported in previous works.
