According to lingdocs dictionary بیان کول's perfective root and stem seem to take the oo- و prefix despite the کول here means 'to make', I wonder what the correct form is.

Good question. بیان کول is a dynamic compound (to DO an explanation/speech), so that takes a و-oo prefix. بیانول is a stative compound (to MAKE _____ explained/spoken) so that will not take the و-oo prefix. In the dictionary you looked up the dynamic version. You can find a more complete explanation of the differences between the dynamic and stative compounds in the "compound verbs" section of the grammar https://grammar.lingdocs.com/compound-verbs/stative-compounds/