Yes, if you are reading all maps for the grammar check, it's normal for it to take some time. You may get rate limited as well by the API. In that case try doing it individually.
It connects to Open AI's API. No data is shared by the app and everything is local.
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Apologies for the oversight, I have added your suggestion in the installation instructions.
OpenAI has a free 5$ trial usage. This should be more than enough to finish a game (or two), unless your game's content is entirely AI generated. It also uses a fine tuned model tailored to RPGM as opposed to a general assistant model by ChatGPT's, so the error resulting to it being cheaper than having to use ChatGPT 4. As the model is further trained, it'll become cheaper and faster to use in the future as well.