We provide an updated inference of the proper motion of M31 using the Gaia DR3 proper motions of bright stars from the disc of M31. By refining the motion of the quasar reference frame, and statistically accounting for the variations in the inferred proper motions obtained across different regions of M31, we demonstrate that these inconsistencies most likely arise from systematic uncertainties. Our updated favoured values for the proper motion of M31 are 46.9 ± 11.7(stat) ± 50.6(sys) µas yr -1 in the right ascension direction and -29.1 ± 9.4(stat) ± 35.6(sys) µas yr -1 in the declination direction, the systematics being determined at a 90% confidence level (the values for M33 are given in the paper). This clearly highlights that the systematics are the dominant source of uncertainty, their magnitudes being comparable to the proper motion of M31 itself. The analysis conducted using Gaia DR2 instead of DR3 revealed that a net reduction in these systematic uncertainties occurred between the two data releases. If similar progress is made with the upcoming DR4, the future Gaia-based estimates could match the uncertainty level of HST, and could be used to refine the dynamics and history of M31 and M33.