According to https://en.cppreference.com/w/cpp/container/vector/data, the underlying pointer is not guaranteed to be nullptr if the size is 0
If size() is 0, data() may or may not return a null pointer.
but does that apply to the default initialized std::vector with no elements? or does that simply state that if all elements of the vector are erased, the underlying pointer may not become nullptr?
Consider the following line:
std::vector<int> fooArr;
int* fooArrPtr = fooArr.data();
is it guaranteed that fooArrPtr is equal to nullptr?
No.
The standard guarantees that a default-initialised std::vector has size() equal to zero, but that doesn't require that data() will return nullptr.
There is nothing in the standard that prevents (and "not preventing" is not equivalent to "requiring") a default-constructed vector having zero .size() and non-zero capacity(). In such a case, it would be feasible for .data() to return a pointer to the allocated memory (which will be non-null, but dereferencing it will still have undefined behaviour since .size() is zero [and allocated capacity is not required to be initialised]).
If you want to test if a vector has zero size, use .size() or .empty(). Don't call .data() and compare the result with nullptr.