More specifically, it'll force you to allocate memory for your recursive functions on the heap (and thus handle the possible resulting OOM condition).
Maybe? Of these features, AFAIK Zig only has function pointers, and they already don't seem to interact very well with other parts of the language. I wouldn't be surprised if they restricted them to comptime-only usage or made "how much stack space does the function need" part of the pointer type or something.
In some circumstances, static proofs are also possible. IIRC it's still an open problem in zig as to what the possible language features will be while keeping this guarantee, but the goal is to be able to have recursion in some circumstances and still provide the possibility of stack-overflow-safety with a performance tradeoff, and to know when you've stepped out of the bounds where that is possible.
Here's a thread I'm at least a year out of date on https://github.com/ziglang/zig/issues/1006
The general philosophy is to give the programmer tools to know what the consequence of a choice will be as far as that doesn't hamstring them overly. Ie. the compiler can tell you when a stack overflow is possible, and it's up to you to decide what to do about it (or whether it is wrong because you know something it doesn't).
At that point I have to wonder what the advantage is over just using explicit checks for overflow on the machine stack though.
It's not 'a split stack' or any other particular solution. You pass in an allocator and it does it whichever way your chose allocator picks.
The goal is to explore sections of design space you're completely ruling out from before you even start.