The MSPSR$\pi$ catalogue: VLBA astrometry of 18 millisecond pulsars

With unparalleled rotational stability, millisecond pulsars (MSPs) serve as ideal laboratories for numerous astrophysical studies, many of which require precise knowledge of the distance and/or velocity of the MSP. Here, we present the astrometric results for 18 MSPs of the "MSPSR$\pi$" project focusing exclusively on astrometry of MSPs, which includes the re-analysis of 3 previously published sources. On top of a standardized data reduction protocol, more complex strategies (i.e., normal and inverse-referenced 1D interpolation) were employed where possible to further improve astrometric precision. We derived astrometric parameters using sterne, a new Bayesian astrometry inference package that allows the incorporation of prior information based on pulsar timing where applicable. We measured significant ($>3\,\sigma$) parallax-based distances for 15 MSPs, including $0.81\pm0.02\,$kpc for PSR J1518+4904 -- the most significant model-independent distance ever measured for a double neutron star system. For each MSP with a well-constrained distance, we estimated its transverse space velocity and radial acceleration. Among the estimated radial accelerations, the updated ones of PSR J1012+5307 and PSR J1738+0333 impose new constraints on dipole gravitational radiation and the time derivative of Newton's gravitational constant. Additionally, significant angular broadening was detected for PSR J1643-1224, which offers an independent check of the postulated association between the HII region Sh 2-27 and the main scattering screen of PSR J1643-1224. Finally, the upper limit of the death line of $\gamma$-ray-emitting pulsars is refined with the new radial acceleration of the hitherto least energetic $\gamma$-ray pulsar PSR J1730-2304.