Is Grok good at prompt-writing outside of Grok itself?

imho, yes. For example, I feed it claude-opus-4.6-thinking thought process slop to identify where it went wrong, and to give me an integrated one-shot prompt. This often works. The only thing it has trouble with is Qwen3.5 but especially on the smaller models, the reasoning crap the latter puts out is ridiculous.

I've generally stuck to the model I'm using to get prompt tips (so Gemini for Gemini, etc).

I always do the opposite. Second opinion > repeated opinion.