As you say, there have been multiple points in history where technological innovation obliterated the livelihood of whole categories of people, from dock workers to sailors to drivers.
Now, automated driving isn't in the "changes everything" category, no more than Diesel engines and containerisation changed everything. Yes, there are still areas which are feeling the impact from this change 50 years ago, but for the most part people moved on into other industries - the service industry in particular.
The thing is, the service industry is being eaten by automation. That does change everything, as without radical change there is not a further category of job for un or semi-skilled labour.
Within the current framework, UBI seems like a sane solution, although finding a way for people to be productive in a way that technology cannot and never can do better would be preferable. The thing is, I'm not certain there is any such thing even in the medium term - even creative and analytic skills are being assumed by AI. Not everybody can be a developer. Even developers will likely be substantially obsolete at some point - we are already at the point where silicon designs silicon with human intervention.
This is no small part of what's troubling the world right now - we have swathes of underemployment like we haven't seen before, and it shows in malcontentedness in the political process.
The other solution of course is to have a hell of a lot fewer humans, but that's unpalatable in terms of implementation.
It's interesting watching the economy contort in on itself in ever decreasing circles of mutation - it's something like Malthusian collapse, as we consume the available pool of productive purposes, leaving a hollowed out civilisation behind.