[docs] ensure pkgdown site index accurately reflects R-package public API (fixes #6444)

[jameslamb]

Fixes #6444.

Fixes LightGBM's documentation builds. These were failing because {pkgdown}, the tool used to generate the R docs site, now raises errors under the following conditions:

• objects mentioned in its config don't exist in the library
• site index is missing any objects exported by the library

How I tested this

Enabled readthedocs builds and saw them succeed:

• build link: https://readthedocs.org/projects/lightgbm/builds/24286998/
• docs: https://lightgbm.readthedocs.io/en/docs-pkgdown-docs/R/reference/

[jameslamb]

thanks @jmoralez !