fix(integrations): sync public API contract and skill commands

[alick-liming]

Summary

• Start from latest CLI main ec0922a and pin SDK PR release: v1.3.27 — monit sparse-field contract + regenerated CLI surface #93 commit 577bf0504904b683160ccc7c7c448883d5661669 via its real Go pseudo-version. No local replace, tag, or SDK main merge.
• Regenerate only the existing Integrations service: retain stored settings, decrypted integration keys, legacy list IDs and permission metadata; support integration_key, is_test and optional plugin test results.
• Add real command-to-HTTP regression tests for list/info, JSON/flag creation inputs, failed plugin-test responses and update header/team clearing.
• Add a generated public integration skill card, route public integrations to it, and correct the old channel card's console-only guidance.

Validation

• Baseline go test -race -count=1 ./... passed before edits.
• New contract tests reproduced missing fields/flags before the dependency and command update, then passed after it.
• go test -race -count=1 ./...
• go vet ./...
• go run ./internal/cmd/skilldoc gen integration
• go run ./internal/cmd/skilldoc check
• git diff --check
• make GCI=/usr/local/bin/gci GOLANGCI_LINT=/private/tmp/cli-lint-tools-20261012/golangci-lint: passed with the repo-pinned v2.11.4 built using Go 1.26; 0 lint issues, race tests and binary build passed. No linter configuration was changed.
• Freshly built CLI binary exercised against a loopback HTTP fixture: list/info/create/update passed, without external API calls or production data.
• Independent simplify and correctness gates.

Scope / Notes

• SDK release: v1.3.27 — monit sparse-field contract + regenerated CLI surface #93 preserves the already-published automation timezone field so changing dependency commits does not drop existing CLI functionality. The pseudo-version has an older numeric base than v0.15.14 because the SDK feature branch predates that tag; the relevant published runtime field is retained and the full CLI suite passes.
• Other generated commands and the command registration file remain unchanged. No new API HTTP clients, request compatibility layer or linter-policy changes.
• Target feat branch has the same latest-main baseline. No main merge is performed.
• Runner and Safari are deferred until real release artifacts/checksums exist.
• No release tags, CDN uploads, sandbox builds, gateway writes or deployment.
• Skill cards are validated with the repository's skilldoc check. The optional generic Codex skill validator could not run locally because PyYAML is unavailable; no claim of that separate validation is made.