  The Legacy Survey of Space and Time (LSST) with the Vera Rubin Observatory
will provide strong microlensing constraints on dark compact objects (DCOs) in
our Galaxy. However, most current forecasts limit their analysis to Primordial
Black Holes (PBH) as the primary DCO candidate. Thus, it is unclear how well
LSST microlensing will be able to constrain alternative models of DCOs which
may possess different galactic spatial profile distributions at a subdominant
DM fraction. In this work, we investigate how well LSST microlensing will
constrain spherical or disk-like galactic spatial distributions of DCOs, taking
into account the effects of extended observing times, baryonic microlensing
background, and sky distribution of LSST sources. These extensions represent
significant improvements over existing microlensing forecasts for LSST in terms
of both accuracy and versatility. We demonstrate this power by deriving new
LSST sensitivity projections for DCOs in spherical and disk-like distributions.
We forecast that LSST will be able to constrain PBHs with one solar mass to
have a DM fraction under $1.6\times10^{-4}$. One-solar-mass objects in a dark
disk distribution with the same dimensions as the Galactic disk will be
constrained below $1.4\times10^{-4}$, while those with $m = 10^5 M_{\odot}$
will be constrained to below $9.3\times10^{-6}$. We find that compressed dark
disks can be constrained up to a factor of $\sim10$ better than ones with
identical dimensions to the baryonic disk. We also find that dark disks become
less tightly constrained when they are tilted with respect to our own disk.
This forecasting software is a versatile tool, capable of constraining any
model of DCOs in the Milky Way with microlensing, and is made publically
available at {https://github.com/HarrisonWinch96/DarkDisk_Microlensing}.
