fix(profiling): require --time-hint for flamegraph and profile-types trace scoping

[AlexJF]

What does this PR do?

Fixes --trace-id scoping for pup profiling explore flamegraph and pup profiling profile-types list.

The backend's traceContext requires traceId, spanId and timeHint (epoch seconds) together, and rejects a null timeHint with a 400. Since #819, pup sent timeHint: null and didn't require --span-id, so both commands failed whenever they were scoped by trace.

• Both commands now build traceContext via the shared trace_context_json helper from feat(profiling): add continuous profiler callgraph exploration #876. The helper requires --trace-id, --span-id and --time-hint together and converts --time-hint (Unix timestamp, RFC3339, relative time, etc.) to epoch seconds.
• New --time-hint flag on both commands (src/main.rs).
• Tests: the profile-types trace test now asserts timeHint, and there's a new flamegraph trace-context request-body test. The helper's own tests are in feat(profiling): add continuous profiler callgraph exploration #876.
• docs/EXAMPLES.md: the profile-types trace example passes --time-hint.

Motivation

Found while adding call graph (#876) and timeline (#877) exploration. Both have the same traceContext contract, and #876 applies this fix for call graph.

Additional Notes

• Stacked on feat(profiling): add continuous profiler callgraph exploration #876 to reuse its trace_context_json helper, so the diff includes feat(profiling): add continuous profiler callgraph exploration #876's commits until it merges. Only the last commit (fix(profiling): require --time-hint ...) is new here.
• --trace-id without --span-id/--time-hint is now rejected client-side instead of with a backend 400. Trace scoping never worked before, so this breaks no working usage.

Checklist

• The code change follows the project conventions (see CONTRIBUTING.md)
• Tests have been added/updated (if applicable)
• Documentation has been updated (if applicable)
• All CI checks pass
• Code coverage is maintained or improved

Related Issues

Fixes trace scoping from #819. Depends on #876.

Plan

# Fix: require --time-hint for profiling trace scoping (flamegraph, profile-types)

Spun off from PROF-16039 (timeline exploration). Full cross-repo plan:
/home/bits/.claude/plans/lets-work-on-https-datadoghq-atlassian-n-nested-dragon.md

## Context

prof-viz-java's `TraceContext` record marks `traceId`, `spanId` and `timeHint` as `@NotEmpty`, and
`FlameGraphExplorationRequest`/`ProfileTypesRequest` validate it (`@Valid`). pup (since #819) sent
`timeHint: null` and didn't require `--span-id`, so `pup profiling explore flamegraph --trace-id`
and `pup profiling profile-types list --trace-id` were rejected with a 400. The backend parses
`timeHint` as epoch seconds (or millis), matching the MCP tool contract.

The same fix landed for callgraph in #876, which introduced the shared `trace_context_json`
helper (validates the three flags together, converts `--time-hint` from any pup time format to
epoch seconds). This branch is **stacked on #876** to reuse that helper.

## Changes

- `src/commands/profiling.rs`: `profile_types_list` and `explore_flamegraph` take `time_hint` and
  build `traceContext` via `trace_context_json`.
- `src/main.rs`: `--time-hint` on `profiling profile-types list` and `profiling explore flamegraph`.
- Tests: profile-types trace-context test now asserts `timeHint`; new flamegraph trace-context
  body test; existing call sites updated.
- `docs/EXAMPLES.md`: profile-types trace example passes `--time-hint`.

## Status

- [x] Worktree `.claude/worktrees/fix-profiling-trace-time-hint`, branch
      `fix/profiling-trace-time-hint` stacked on `feat/callgraph-exploration`
- [x] Implementation + tests + docs
- [x] fmt / clippy / `cargo test profiling::` — 40 pass
- [x] Commit + push to `origin`, draft PR into DataDog/pup:main

Prompts

# Prompts log — profiling trace time-hint fix (spun off from PROF-16039)

1. (PROF-16039 context) "Lets work on https://datadoghq.atlassian.net/browse/PROF-16039, following
   similar patterns to https://github.com/ddoghq/profiling-backend/pull/9070 and
   https://github.com/ddoghq/dd-source/pull/102914"
2. "Can't we sign with my personal SSH key, open a PR against my fork AlexJF/pup and open a draft PR
   from there to upstream?"
3. "try again"
4. Asked whether to open a separate fix PR for the same timeHint bug in merged flamegraph /
   profile-types trace scoping: "yes do"

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