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GH-35875: [R] Update Readme (#40148)

### Rationale for this change

#35875  #35082 and #32895 make a number of recommendations to update the the Readme

### What changes are included in this PR?

Rewording and reorganizing the Readme and sidebar.

### Are these changes tested?
n/a

### Are there any user-facing changes?

Yes 

* Closes: #35875

Lead-authored-by: David Greiss <david.dgreiss@gmail.com>
Co-authored-by: Nic Crane <thisisnic@gmail.com>
Co-authored-by: Bryce Mecum <petridish@gmail.com>
Signed-off-by: Nic Crane <thisisnic@gmail.com>