Description states:

[ - Jump past matching ] if value at current cell is 0

Hence:

• start with leftmost cell. that is 0
• move past matching ]. that is past the end.
• terminate, since going out-of-bounds is termination condition
• return unchanged tape

That makes sense. However, such tests would invalidate some (incorrect) user solutions. It doesn't matter if arrays are of size 4 or 5 but it does matter if one array is 5 and the other 4.

love the comments

I like the comments and variable names

Shouldn't all of them do that? I was wondering if there is a reason why they don't.
I think it is important thing to think about (that arrays may have different length) and therefore to test for. Arrays could be empty too but I guess the description vaguely hints that there will be integers (and only) inside.
Do you think it would make sense for me to extend the test cases? Assuming I am allowed to do so.

With code formatted like that hardly anyone will bother to try to read it. Use markdown as suggested.

I find it hard to follow your logic. Maybe it is too late/early for me.

One thing I did notice is that this two codes differ.
The local one is actually invalid because the function does not return anything (should return bool). Not to mention the stray include at the beginning and lack of necessary ones.
You can't interchange return and cout. Those do not have the same behaviour. return stops execution of a function, cout does not.

The problem with passing the kata is somewhere else though. Try to test (({{[[]]}})) as suggested. Follow the code execution or try to follow the algorithm yourself, possibly on a paper. There is a problem with your logic or the expression of said logic.

I don't believe that interchanging int and bool is a good idea.

1. using namespace std before include's feels wrong to me but I can't find what possibly horrible things will happen if you use it that way (I wouldn't use it at all, but that's just me).
2. why do you need iostream, fstream, cmath and cstdlib?
3. what is the purpose of str variable? You could make ans from st. Not that the copy is necessary at all in my opinion.
4. by using erase you are copying the remaining part of the string every time and possibly cause memory reallocations. Not to mention that you already copied the string twice before the loop starts. You could use std::remove_copy_if (like here https://codereview.stackexchange.com/questions/11203/most-efficient-way-in-c-to-strip-strings) or gradually recreate the string using += as many other people have done here.

why do you include (need) iostream?