Several metres is a slight exaggeration, not enough to matter for such purposes anyway, and may even already be taken into account.
From 1994 to 2020, the physical difference was about 1.8m (that’s comparing it with another map projection, but what else can you do?), so in what should be the worst case scenario (if they were actually using accurate maps which I think would reasonably imply nothing worse than GDA94), you should have less than two metres of drift, and the only time that’s ever going to matter is when you want to identify service roads distinctly from the adjacent main road. And continental drift is probably still even within your car’s GPS sensor’s margin of error. No, I don’t think you can reasonably blame continental drift for road jumping; it’s typically going to be bad map data, with roads simply being marked in the wrong place. I have a 2010 Mazda 3 with maps from 2010, and out in the country its maps are commonly out by 10–20 metres, with the largest deviation I’ve observed where I know the route hasn’t changed in at least the last couple of decades being about 150m.
To my mind, the real doozy about these geodetic datums is that they’re time-dependent, including a prediction of continental drift. I have no idea whether the car’s maps system does do that, but it should be doing something like storing all coordinates in GDA94, rendering in MGA94, and projecting GPS coordinates into that coordinate space, so that continental drift’s effects are negligible.
(I’ve wondered casually about continental drift in map projections before, but never gotten round to investigating the reality of it. I didn’t realise they could be time-dependent until today. I must get round to asking my dad about it, as he’s done quite a lot of maps and projections stuff.)