Fixes #44293.

This replacement carries forward the useful work from #44824, #48887, and #49913 with attribution to @tianxingleo, @soyames, and @yil337. The previous PR branches are closed/unmerged or uneditable, so Clownfish should land the narrow remaining fix separately while preserving source PR credit.

Planned changes:

• keep format:docs and format:docs:check routed through the shared docs formatter helper;
• invoke the npm-installed oxfmt shim safely on Windows, including .cmd handling;
• preserve command-line batching/chunking for large doc sets;
• print explicit spawn diagnostics for git and oxfmt failures;
• add focused tests for mode selection, batching, spawn-error handling, and Windows shell/shim behavior.

Validation:

• pnpm -s vitest run test/scripts/format-docs.test.ts
• pnpm format:docs:check
• pnpm check:changed

Clownfish 🐠 replacement reef notes:

• Cluster: ghcrawl-156809-autonomous-smoke
• Source PRs: build(docs): make check:docs PowerShell-compatible #44824, Fix/docs format check windows clean #48887, docs: make format check PowerShell-friendly #49913
• Credit: Credit @tianxingleo for the original cross-platform scripts/format-docs.mjs direction in build(docs): make check:docs PowerShell-compatible #44824.; Credit @soyames for the more complete Windows-clean formatter/check test direction in Fix/docs format check windows clean #48887.; Credit @yil337 for the PowerShell-friendly docs format check approach and command-line chunking direction in docs: make format check PowerShell-friendly #49913.; Mention the maintainer repair context on Fix/docs format check windows clean #48887 and preserve contributor attribution in the replacement PR body.
• Validation: pnpm -s vitest run test/scripts/format-docs.test.ts; pnpm format:docs:check; pnpm check:changed

fish notes: model gpt-5.5, reasoning medium; reviewed against 5522f06.