Whilst there isn't an API to find out stack size directly, contiguous virtual address space must be reserved up to the maximum stack size - it's just that a lot of that space isn't committed yet. You can take advantage of this and make two calls to VirtualQuery.
For the first call, pass it the address of any value on the stack to get the base address and size, in bytes, of the committed stack space. On an x86 machine where the stack grows downwards, subtract the size from the base address and VirtualQuery again: this will give you the size of the space reserved for the stack (assuming you're not precisely on the limit of stack size at the time). Summing the two naturally gives you the total stack size.
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