I wonder whether a list module wouldn't be better for this, both because meta=siteinfo is already rather overgrown and because the list module could be made to be used as a generator.

To clarify, you want to retrieve:

• The category name (Pages where template include size is exceeded) as plain text
• The category description (The page size is bigger than <code>$wgMaxArticleSize</code> after expanding all the templates, so some templates were not expanded.) as plain text

Is that correct?

Tracking categories are defined by adding a message key name to $wgTrackingCategories. The minimal version would be to output the value of that in meta=siteinfo.

But chances are any client requesting these isn't going to care much about the message key name, they'll probably want to know the actual category titles on-wiki to look at. They may even want to use it as a generator. Use as a generator would call for a separate (list) module, which can return both the key and the category title.

The description's message key is derived from the category's key by appending "-desc", and list=allmessages already has the infrastructure to fetch that. In general we try to keep UI messages other than errors and warnings out of the rest of the API responses. So I'd recommend not including that part.

@Anomie so to double check, just retrieve the name of the categories (as plain text)?

Just the categories and keys, not their descriptions.

A single tracking category can have multiple names, for example broken-file-category may be Articles with missing files, Templates with missing files or Pages with missing files‎ on enwiki (depending on the namespace). This means that the the result of this API module should contain an array, for example instead of something like

[
	{
		"name": "broken-file-category",
		"category": "Pages with missing files‎",
		"The page contains a broken file link (a link to embed a file when the file does not exist)."
	}
]

it should be along the lines

[
	{
		"name": "broken-file-category",
		"category": ["Articles with missing files", "Templates with missing files", "Pages with missing files‎"],
		"The page contains a broken file link (a link to embed a file when the file does not exist)."
	}
]