There are some plugins not having a README file in the project, for those, we have the EXCLUDE_PLUGINS here to be able to maintain or own HTML file:
https://github.com/geany/plugins.geany.org/blob/master/gencontent.sh#L71
I've just removed the latex plugin from this exclude, as there is a README now (which is quite minimal, but hey, there is one!). @frlan you could update it to have a bit more content if you wish the website to display more then.
In the other points, @eht16 is right:
There is no automation to delete a plugin from the website until now and has to be done manually. Also, I think this will not be trivial to implement. As it doesn't happen that often that a plugin is deleted from the Geany plugins project, I think it will be fine if you open an issue and I will take care of this then.
Anyway, a pull request for automating this of course is always appreciated.