docs: add a live-validated Calls SDK example and troubleshooting

[JJasonSun]

Summary

Add a runnable Python Calls example that saves the original request before submission and the returned Call ID before polling. start requires a new private run directory; resume retrieves the saved call without submitting another create request. Missing create responses stop with recovery guidance. Quickstart links the official testing hotline and explains setup, costs, saved data, and result interpretation. Errors adds a provider/configuration/billing troubleshooting table.

The region-table reader accepts both published fifth-column names (Default Line and Line Region) and preserves the source wording. Other shape and content validation remains in place.

Refs CALLE-AI/awesome-phone-call-agents#407. The separate sandbox capability request is tracked in CALLE-AI/awesome-phone-call-agents#627.

API contract

Not changed. Uses the published calle-ai==0.7.0 SDK and existing Calls recovery contract. No package release or changeset.

Validation

• On September 14, 2026, ran python examples/calls.py start <private-run-directory> --phone <authorized-test-hotline> locally with Python 3.12 and calle-ai==0.7.0 against the real service. One attempt connected at 08:51:04 UTC and ended at 08:51:14 UTC. The command returned zero with status: completed, task_completed: true, and heard_greeting: yes. The greeting summary matched both callee transcript turns.
• Ran python examples/calls.py resume <same-directory> in a separate process. It returned zero and retrieved the same saved Call ID and terminal result. Call data, destination, and credentials are excluded from the PR.
• python -m unittest discover -s examples -v passed. Supplemental cases cover a rejected create, non-JSON gateway response, polling timeout after saving the ID, repeated-start refusal, resume without another POST, and a null structured result on a terminal failed call.
• Full local pnpm run validate passed: typecheck, production build using the current upstream region source, static artifact checks, 11 deployment tests, and all 22 browser tests. Both new guide sections were visually checked. git diff --check passed.

This verifies the SDK call-to-result flow against the official test recipient. Webhook delivery, live quota/provider failures, business workflows, and sandbox determinism or free calling were not tested.

Checklist

• I kept the change focused and public-facing.
• I removed secrets, private URLs, phone numbers, and customer data from the documentation and evidence; offline tests use a fictional number.
• No OpenAPI change.
• I added recovery checks for the executable example.
• I added screenshots for visual changes.
• I ran pnpm run validate.

[JJasonSun]

Publication is verified: the runnable Python example is linked from Quickstart, and the troubleshooting table is available in Errors. PR #61 repaired the deployment-list pagination check, and the production deployment passed.

This supplies the published documentation tracked by CALLE-AI/awesome-phone-call-agents#407.