claude-web-console: render stored transcript in the viewer

[studykit]

Description

Read a selected stored session transcript and render it in the viewer, so a
stored session displays the same way a live one does. This turns the session
picked in the browse subtask into readable, richly rendered output.

Context

• Stored transcripts are JSONL: one JSON object per line, each a typed record
  carrying at least type, timestamp, and sessionId (observed types
  include non-visible bookkeeping records such as queue-operation). The exact
  set of record types and their content fields is enumerated at implementation
  against real transcripts.
• This stored shape is not the same as the live payloads the viewer
  consumes today: the hooks POST {type:"user"...},
  {type:"assistant_delta"...}, {type:"turn_end"} to /event. Rendering a
  stored transcript therefore needs a mapping from stored JSONL records to the
  render events the viewer already understands.
• The viewer's renderer registry is the markdown-it fence rule (markdown,
  math via KaTeX, PlantUML via the local PicoWeb bridge); stored content should
  render through that same registry rather than a second rendering path.

Acceptance Criteria

• A selected stored session renders its user prompts and assistant messages in
  transcript order.
• Renderable fenced blocks (markdown, math, PlantUML) render identically to the
  live path, reusing the existing renderer registry.
• Record types with no user-visible output are skipped without breaking the
  render.
• A long transcript loads and displays without hanging the viewer.
• Malformed or partially written lines are tolerated (skipped) rather than
  aborting the whole render.