Yes, and it is the first real step toward governance. A style guide is where an organization writes down what good API design looks like for them: naming, path structure, error format, versioning, pagination, filtering, date formats, casing, status code usage. Made consistently, these decisions produce a coherent portfolio. Made independently by each team, they produce chaos that no gateway can fix later.
You do not have to invent it. Heroku’s HTTP API design guide, Google’s API design guide, and the collected guides at API Stylebook are all public, and starting from one of them is faster and better than a blank page.
The complication I would not skip: a style guide on its own is necessary but not sufficient. A document listing conventions, disconnected from anything that enforces them, is a document that may never change what gets shipped. The style guide has to be connected to machine-readable rules that run in the editor and the pipeline, and it has to be tied back to the policies that explain why each convention exists.
The chain is: policy explains why, style guide articulates what, rules enforce it, engines run it, guidance helps people follow it. Start with the style guide, but plan the rest of the chain from day one.