chore: sync generated client with staging OpenAPI

[leo-notte]

Summary

• regenerate the Go API client from the current staging OpenAPI schema
• remove managed-auth models and operations that are no longer published

This fixes the notte-cli matches staging OpenAPI failure in nottelabs/monorepo#2076.

Verification

• go test ./...
• make check

[greptile-apps]

Greptile Summary

This PR regenerates the Go API client against the staging OpenAPI schema and removes managed-auth types and operations that are no longer published.

• Removes the managed-auth models, enums, request parameters, request builders, client methods, and response wrappers.
• Retains the remaining generated API surface while re-emitting it at shifted locations.
• Adds no focused unit or integration coverage for the schema-surface change.

Confidence Score: 4/5

The PR appears safe to merge, with the non-blocking concern that the generated API-surface removal has no focused regression coverage.

The removed managed-auth symbols have no identified callers elsewhere in the repository, and no concrete request-builder or response-parser mismatch was established; only missing change-specific test coverage remains.

Files Needing Attention: internal/api/client.gen.go

Important Files Changed

Filename	Overview
internal/api/client.gen.go	Regenerates the typed API client and consistently removes the unpublished managed-auth surface; no remaining repository callers were found, but the change adds no regression test.

Prompt To Fix All With AI

### Issue 1
internal/api/client.gen.go:130
**Add schema-removal regression coverage**

This regeneration removes the managed-auth API surface without adding focused unit or integration coverage, leaving future accidental removal of a consumed operation to be caught only by the existing broad build and generation checks.
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