The object notation format that's going to win is the one that's going to maximally support LLM output. I've come across BAML before, but it's not widely used for some reason.
Today JSON is winning, but for more complex structures, there's still syntax issues in output. XML does reasonably well (given the deep react jsx/HTML in the training corpos), so perhaps that will make a comeback.
Are there benchmarks on this? I think the SOTA models are fine -- they can work with most models, but the fun is that models that are 90% of SOTA performance and cost 90% less - which output format do they work best with. This is where the winner will be found.
TLDR: probably JSON or XML will remain the config format for a while.