The type std::size_t is defined to be a numeric type that can represent the size of the largest possible object (say, N bytes).
The largest object could be an array, and the array with the most possible objects is therefore an array of N chars.
So, std::size_t makes sense for array indexes and dimensions too.
You should stick to this convention as much as possible, because otherwise you potentially introduce bugs:
std::size_t is commonly used for array indexing and loop counting. Programs that use other types, such as unsigned int, for array indexing may fail on, e.g. 64-bit systems when the index exceeds UINT_MAX or if it relies on 32-bit modular arithmetic (cppref)
We could have had a std::index_t instead, but it would have been the same as std::size_t, so that's pointless.