chore: make extCore and customEliminators public for Batteries

[kim-em]

This PR restores two declarations to public, that were made non-public in #10699, apparently breaking Batteries.

[leanprover-community-bot]

Mathlib CI status (docs):

• ❗ Batteries/Mathlib CI will not be attempted unless your PR branches off the nightly-with-mathlib branch. Try git rebase 2f93363752104c7ac26a2af06fed5bff66ee74b5 --onto 14ff08db6f651775ead432d367b6b083878bb0f9. You can force Mathlib CI using the force-mathlib-ci label. (2025-10-15 23:45:20)

[leanprover-bot]

Reference manual CI status:

• ❗ Reference manual CI will not be attempted unless your PR branches off the nightly-with-manual branch. Try git rebase 2f93363752104c7ac26a2af06fed5bff66ee74b5 --onto d3dda9f6d4428a906c096067ecb75e432afc4615. You can force reference manual CI using the force-manual-ci label. (2025-10-15 23:45:22)