[3.11] GH-97950: Use new-style index directive ('builtin') (GH-104164) (#104221)

GH-97950: Use new-style index directive ('builtin') (GH-104164)

* Uncomment builtin removal in pairindextypes

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

* Use new-style index directive ('builtin') - Extending

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

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

* Use new-style index directive ('builtin') - Tutorial
(cherry picked from commit f5088006ca8e9654fbc3de119462f0ab764e408b)

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