That's not only wrong in itself, but totally orthogonal.
A binary search implementation should still work, regardless of the array length, or have the limitation documented.
And of course an array "with length over a billion" can be totally valid, depending on the use case, your tradeoffs, available memory, etc. It could even be the optimal data structure for some use cases.
If you really needed it in memory you’d use one of the file APIs that will map it and present a direct byte buffer view over that memory.
Those APIs use long as their offset unlike the 32 ints used by arrays, and would avoid having to copy the data into some other object.
There has been some discussion over the years about how arrays could be changed in the JVM to support longer lengths, but doing so without breaking existing code and while providing truly useful functionality without providing obvious footguns isn’t as easy as you might think.
Relational databases often require searching and sorting gigabytes of data to answer queries (sometimes larger than RAM if e.g. k-way merge sort is used) so it doesn't seem that far-fetched, especially given that there are database systems written in Java.
A binary search implementation should still work, regardless of the array length, or have the limitation documented.
And of course an array "with length over a billion" can be totally valid, depending on the use case, your tradeoffs, available memory, etc. It could even be the optimal data structure for some use cases.