Help converting sha256 to 32-bit stream
No, you don't have to convert to a 32-bit string.

A "32-octet octet stream" means an octet stream with a length of 32 octets. An octet stream is also known as a byte array. In older times bytes could have different lengths (7 or 9 byte lengths have existed). An octet is always 8 bits; nowadays octets and bytes should be considered synonyms.

So basically they are saying: treat the bit string as a stream of octets of the same length (as $32*8=256$), then base-64 encode it. Now most crypto libraries already treats the output of SHA-256 as byte array (octet stream). So you just are left with encoding the output to base 64.

One small warning: some crypto libraries already contain encoding internally. You will need to explicitly choose raw byte output for those libraries, unless you can specify base64, of course.