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GH-14969: [R][Docs] Enable pkgdown built-in search (#36374)

### Rationale for this change

Enable local search of pkgdown site.

### What changes are included in this PR?

Remove some files that are not currently in use.

### Are these changes tested?

There is no test, but the following functions can be run to verify that the site is working properly.

```r
pkgdown::init_site("r")
pkgdown::build_search("r")
pkgdown::build_home("r")
```

### Are there any user-facing changes?

No. Document changes only.
* Closes: #14969

Authored-by: SHIMA Tatsuya <ts1s1andn@gmail.com>
Signed-off-by: Nic Crane <thisisnic@gmail.com>