[3.13] gh-121596: Fix Sharing Interpreter Channels (gh-121600)

This fixes a mistake in gh-113012 and adds a test that verifies the fix.

(cherry picked from commit 35a67e36aa7cb0fc915771327f58bb0c70213867, AKA gh-121597)

Co-authored-by: Eric Snow <ericsnowcurrently@gmail.com>