chore(site): rebuild the payload after the advanced-modeling regen

`site-payload.json` embeds excerpts from `examples/advanced-modeling/src/generated/**`,
so regenerating those made the committed payload stale and `gate_site_payload` red. Four
lines: the JSDoc block inside the quoted excerpts.

The ordering is the lesson — the payload has to be rebuilt AFTER every generated-output
regen, not alongside the first one. Changing what codegen emits means four separate
regens, each with its own gate: the codegen-ts goldens, `regen:showcase`, `site:payload`,
and `examples/advanced-modeling`.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UcDcQmAVYzYjkVGVj23mt4

Author: dmealing