If Pete's process appears to be an optimum one, he would be expected to independently submit a patent proposal for the synthetic route. Dana and Shirley are not inventors because they did no more than follow Barb's directions and applied a known method. Either the Beta Company had chosen not to patent it, or the XYZ Company is paying a royalty for its use. Authorship will be decided by the scientists. Company practices may often control what is done.
Some companies tend to include anyone who had any connection with the work.
Such a lab may choose to include all four workers as authors. Academic readers often complain that the overly long lists of contributors is unrealistic, and does not convey the identity of the true authors. A possibly more correct solution would be for Barb and Pete to author the paper and include an acknowledgment to the help of Dana and Shirley. In this case, the new assay is critical to demonstrating the utility. They would, in this case, certainly be included as authors.