Sub-issue of #679.

Goal

Introduce a typed Pydantic model representing the unified shape of status_data for kernels and sessions, covering all four branches: kernel, session, scheduler, and error.

Scope

• New file under src/ai/backend/common/dto/manager/v2/ (likely status_data.py or per-entity files in kernel/ and session/).
• Pydantic v2 model(s):
  • KernelStatusBranch — {exit_code: int}
  • SessionStatusBranch — {status: str}
  • SchedulingPredicateModel — {name: str, msg: str | None}
  • SchedulerStatusBranch — {msg, retries, last_try, passed_predicates: list, failed_predicates: list}
  • ErrorDetailModel — typed error detail (mirror of manager/exceptions.py:ErrorDetail)
  • ErrorStatusBranch — {errors: list[ErrorDetailModel]} (the normalized list shape; see #(step-2 sub-issue))
  • Top-level KernelStatusData aggregating all branches as optional fields.
• Unit tests under tests/common/dto/manager/v2/ validating round-trip parse/serialize for representative payloads.

Non-goals

• This issue does NOT change wire format on the producer side. That's the next sub-issue.
• No changes to v2 REST/GraphQL DTOs to expose status_data yet.

Acceptance criteria

• Pydantic model importable from ai.backend.common.dto.manager.v2.
• Model parses both legacy single-error shape and new errors-list shape (tolerant reader).
• Tests cover all four branches and both error shapes.
• Pants quality gates pass.

JIRA Issue: BA-5864