[3.11] GH-97950: Use new-style index directive ('object') (GH-104158) (#104159)

GH-97950: Use new-style index directive ('object') (GH-104158)

* Uncomment object removal in pairindextypes

* Use new-style index directive ('object') - C API

* Use new-style index directive ('object') - Library

* Use new-style index directive ('object') - Reference

* Use new-style index directive ('object') - Tutorial
(cherry picked from commit 6ab463684b9d79880d98cd1f1406aa86af65985e)

Co-authored-by: Adam Turner <9087854+AA-Turner@users.noreply.github.com>