fix: correct template request return body

[dobrac]

Note

Adds POST /v3/templates with a new minimal response, deprecates older template endpoints (now returning TemplateLegacy), refactors handlers to be context-aware, and updates OpenAPI, generated clients, and tests.

• API (v3):
  • Add POST /v3/templates with routing/middleware and handler PostV3Templates.
  • Introduce TemplateBuildRequestV3 and TemplateRequestResponseV3 models.
• Deprecations/behavior:
  • Mark legacy endpoints (/templates, /v2/templates, related build-start routes) as deprecated; their 202 responses now return TemplateLegacy.
• Handlers:
  • Implement v3 build flow via requestTemplateBuild helper.
  • Make GetUserAndTeams and GetTeamAndLimits accept context.Context; update all call sites.
• OpenAPI/Codegen:
  • Update openapi.yml; regenerate server/types/spec and integration client to include v3 endpoint and response/model changes.
• Tests:
  • Switch integration tests/utilities to use POST /v3/templates and new response types.

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