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I'm not sure if the model (under its temperature/other settings) produces deterministic responses. But I do think models' style and phrasing are fairly changeable via AGENTS.md-style guidelines.

5.4's choice of terms and phrasing is very precise and unambiguous to me, whereas 5.3-Codex often uses jargon and less precise phrases that I have to ask further about or demand fuller explanations for via AGENTS.md.

So sharing markdown files is functionally useless, or no?

No it's just stochastic like everything about LLMs. The md file will bias results towards a certain set of outcomes.

In case you missed it, json is less likely to be written over than markdown by agents- something to do with the structure being more rigid

you probably can't and asking agents.md to "make it clearer" will likely give you the illusion of clearer language without actual well structured tests. agents.md is to usually change what the llm should focus on doing more that suits you. Not to say stuff like "be better", "make no mistakes"