  On 29 May 2023, the LIGO Livingston observatory detected the
gravitational-wave signal GW230529_181500 from the merger of a neutron star
with a lower mass-gap compact object. Its long inspiral signal provides a
unique opportunity to test General Relativity (GR) in a parameter space
previously unexplored by strong-field tests. In this work, we performed
parameterized inspiral tests of GR with GW230529_181500. Specifically, we
search for deviations in the frequency-domain GW phase by allowing for agnostic
corrections to the post-Newtonian coefficients. We performed tests with the
Flexible Theory Independent (FTI) and Test Infrastructure for General
Relativity (TIGER) frameworks using several quasi-circular waveform models that
capture different physical effects (higher modes, spins, tides). We find that
the signal is consistent with GR for all deviation parameters. Assuming the
primary object is a black hole, we obtain particularly tight constraints on the
dipole radiation at $-1$PN order of $|\delta\hat{\varphi}_{-2}| \lesssim 8
\times 10^{-5}$, which is a factor $\sim17$ times more stringent than previous
bounds from the neutron star--black hole merger GW200115_042309, as well as on
the 0.5PN and 1PN deviation parameters. We discuss some challenges that arise
when analyzing this signal, namely biases due to correlations with tidal
effects and the degeneracy between the 0PN deviation parameter and the chirp
mass. To illustrate the importance of GW230529_181500 for tests of GR, we
mapped the agnostic $-1$PN results to a class of Einstein-scalar-Gauss-Bonnet
(ESGB) theories of gravity. We also conducted an analysis probing the specific
phase deviation expected in ESGB theory and obtain an upper bound on the
Gauss-Bonnet coupling of $\ell_{\rm GB} \lesssim 0.51~\rm{M}_\odot$
($\sqrt{\alpha_{\rm GB}} \lesssim 0.28$ km), which is better than any
previously reported constraint.
