Thread safety of char[] is the cause of the bug, but the effect is that String instances can violate their invariants, which they shouldn't even in case of thread-unsafe code.
In my opinion the abstraction is leaky but everything works according to the spec.
I might tell you about another "bug" and "invariant violation" which is possible but is not a bug. Try to use Sets or Maps with keys having broken hashcode.
I can't agree with this analogy. This is not a defective user implementation of hashcode; it is a defective platform implementation of equals (and starts with, etc.).
Again, this is not a bug. There are many, way too many places in standard library which are thread unsafe. Some of these are actual bugs, but not this one. If Java originally moved in Odersky's direction that won't be the case but now it's way too late to point fingers at these "quirks".
In order to properly fix these issues the whole standard library has to be redesigned around immutability and, probably, immutable arrays must be supported at VM level.
This is not going to happen.
But it's specified that standard Java classes are thread unsafe by default. So this is a specified behaviour.
It is weird Java considered it a bug, I expect it to be resolved as "wont do"