docs: deduplicate, trim and resync the repo documentation

[vidit-admin]

Summary

Doc-only cleanup across docs/, the root meta files, the GitHub templates and video/README.md. About 2,150 lines removed and 1,370 added; docs/api.md drops from 24,800 to 15,400 words.

• Drift fixes, each checked against the code: the api.md error envelope and codes, the read-quota list, the POST /tags duplicate behaviour, response examples, the pagination scope; the data-model.md ER diagram (4 missing tables, conflicts.tier), uuid4 primary keys, a stale migration id; the engineering.md Postgres version, auth wall, docs-pairing exemption, MkDocs deploy; the README invite flow; the CONTRIBUTING CI job list; the PR template anchors.
• Deduplication: one shared event-form field table and error table in api.md, one example per schema, rate limits stated once; the FE/BE mirror list moves from AGENTS.md into the engineering.md#hand-kept-mirrors table; README links to engineering.md and CONTRIBUTING instead of repeating them; bucket facts live in backups.md.
• Trimming: design.md compressed with every rule kept; video/README reduced to one table row per promo, with the shooting rationale moved into the record-*.js header comments (comments only).
• Public-doc hygiene: removes hosting costs, user counts, monetization intent and personal fixture values; removes history narrative and dashes used as punctuation.
• New diagrams: the api.md request pipeline and event lifecycle, the backups.md flow, the design.md collections flow; all render with mermaid-cli. The AGENTS.md render command now uses --size 1500, since mermaid-cli 12 rejects -w.

planning/ is out of scope for this PR.

Test plan

• Every relative link and anchor in the changed docs resolves (script check).
• Every added or edited Mermaid diagram renders locally.
• node --check passes on the edited video/record-*.js files.

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