Running the engine as a plugin
You might want to prefer the GPT approach to run the engine since ChatGPT Plugins seem to be deprecated by OpenAI - it seems that they don't want new plugins in favor of GPTs, and since 11/2023 they seem to have broken local plugin development for good. But I've happily used it as a plugin for quite a while, so here you are.
Register the engine as an unverified plugin
For this you have to make the engine available via https, open the plugin store in ChatGPT and click “Install unverified plugin”. Then you have to enter the domain name at which the engine is accessible from the internet.
Once you've added the plugin, you can test it in the ChatGPT interface. Try asking the AI to list the files in the directory, read a specific file, write to a file, or execute a specific action after setting up some actions in a .cgptcodeveloper directory in the directory you're running it. If everything is set up correctly, the AI should be able to perform these operations using the plugin.
Run it locally as a plugin developer
That used to be the easiest way to run the engine as a plugin, but when I tried it since 11/2023 it didn't work anymore and I'm not sure whether they will fix it since you cannot eveen register yourself as a plugin developer anymore. But for the record: if you open the plugin store there is a link “Develop your own plugin”. There you have to enter e.g. localhost:3002 if you run the engine with this port, and it should work. (Currently I can register the plugin that way, but when trying to use it ChatGPT says “Plugin not found”.)