Can they handle construction zones where lanes split all over the place and speeds change? I'm guessing no. Based on the constant amount of scuff marks along the guards of the 5 freeway and pretty much every other freeway in California I'm assuming thats a hard challenge even for human drivers.
All they need to do is recognize a construction zone a minute ahead of time and get the human to take over. This would allow level 4 through construction zone. Level 4 is self driving "in the easy parts", and give humans enough time to take over in the "hard parts" (level 5 is everywhere, and as you note a much harder problem). Note though that you can't just stop driving, you need to allow time for the human to figure out what it going on, how to properly have humans take over is itself a hard problem.
For what it’s worth, the one thing my Tesla has been consistently good at is picking the correct lines out of a jumble of nonsense on the road.
I’ve used AP heavily in highway construction zones, and at night with bad visibility, and in inclement weather, and in combinations of the above. AP does better than I can manually do at picking the correct set of road marks to follow, even in cases where the construction has left partial incorrect marks underneath / conflicting_with the right ones.
AP has a ton of other issues of varying levels of severity, but if you’re asking “can I trust it in a construction zone”, I’d say yes based on my usage.
No, they fail spectacularly at ad-hoc road work lane setups or setups where the "official" lanes are temporarily blacked out. I think that was the cause of the Tesla smashing into a freeway median a couple years ago.