Defining owners and processes for tooling
For tooling to be effective, it really needs two fundamental things. The first is an owner for that tool, while the second is for processes to be defined and documented for that tool.
The owners of your tooling are responsible for defining how the tool is used, what scenarios it helps resolve, defining processes for how to use parts of the tool, and providing ownership in terms of the infrastructure and any costs behind it. You may split tool ownership between business ownership to manage the costs, infrastructure required, or license costs and a technical owner who looks after the knowledge articles and processes for how to use the tool.
Considerations should be made regarding the tool's life cycle at this point as well. While talking about test tooling, the following article from Cania Consulting (https://cania-consulting.com/2019/10/25/software-testing-tool-basics/#Testing_tool_life_cycle) provides a good explanation of the tool...