docs: add OpenAdapt Execute API integration guide

[abrichr]

Summary

• add the smallest useful private-pilot Execute API guide
• cover service bearer authentication, the Types 0.8 request, idempotency, lifecycle states, terminal outcomes, polling, and receipt validation
• document the stable signed-body webhook verification, at-least-once delivery, deduplication, and ordering rules
• link the guide from the private-pilot brief and the Docs navigation

Dependencies

• This PR is based on and depends on Docs PR docs: define OpenAdapt Execute private pilot #99 at exact head 0e752b4.
• Do not merge this PR before docs: define OpenAdapt Execute private pilot #99.
• Do not merge or publish this guide before Cloud PR #223 accepts and deploys the final webhook delivery contract.
• One isolated dependency block marks the final transport header names. It must be replaced from the accepted #223 contract. The guide does not invent names from a superseded PR head.

Verification

• independent exact-contract review: ACCEPT
• 124 tests pass
• Docs validation passes
• offline published-version checks pass
• strict MkDocs build passes
• no copy- or markup-pinning frontend tests were added