feat(public): expose finalized recording on the public show / re-listen page

[anneoneone]

Part of #239 (deferred — later).

Problem

Public pages (re-listen.html, public show view) have zero visibility into recordings — only hardcoded SoundCloud tiles. No status, no download.

Scope (deferred)

• Surface the finalized recording (status + download or embedded player) on the public show page once the admin/backend path (other fix(live recording): live recordings are stored but cannot be used #239 sub-issues) lands.
• Larger effort: there is currently no vanilla-TS per-show public page.

Acceptance

• Public visitors can see/play/download a show's finalized recording where appropriate.