In our organization we developed a playbook as you described, which is composed of all the IMO governance documents needed to ensure a successful integration for our business. The foremost document we used was the framework, which contained information from every single functional area of our organization and the key tasks/documents/decisions needed to integrate each area. In addition to the framework we had our RAID log, scorecard and integration plan deck for communication with the business. It was a painstaking process, but having been through multiple mergers, no two are equal, and the templates were adjusted to accommodate each integration.
Thus the answer to your question is a yes and a no. There is no true “perfect” playbook, you may have a starting point with some good bones in your documents, but you will need to be flexible and adjust for each deal separately.