I think we should omit these suffixes.
Not everything is a plugin(/module/extension/…)
There are cases where a solution is required to work with a software, but it doesn’t necessarily have to be a plugin (or similar).
Example question: Offline WordPress post editor/creator - Here a solution is required to work with WordPress, but it can’t be a WordPress plugin. So tagging this with wordpress-plugin is obviously wrong, so we need a wordpress tag.
But when we need a wordpress tag anyway, …
… what do we gain by having an additional -plugin tag?
Experts in WordPress plugins are very likely also experts in WordPress, and they probably know cooperating tools.
Of course there are cases where a user explicitly needs a plugin (and doesn’t want to use a separate tool), but this is information which can be specified in the question. I don’t think this case necessitates an additional tag.
Some programs have plugins and extensions
For example, Mozilla Firefox has "add-ons" and "plugins". Following the suffix model, we would need three tags:
I guess in many cases, users don’t care if a solution is technically a plugin, an extension, a user script or a different tool. The tag firefox could cover all these cases.
So I propose to omit any suffixes and use the software name as tag value: