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GH-43044: [R] So-called non-API entry points (#43173)

### Rationale for this change

CRAN 

### What changes are included in this PR?

Remove so-called non-api calls

### Are these changes tested?

With tests

### Are there any user-facing changes?

Hopefully not

**This PR contains a "Critical Fix".**
* GitHub Issue: #43044

Authored-by: Jonathan Keane <jkeane@gmail.com>
Signed-off-by: Jonathan Keane <jkeane@gmail.com>