chore(deps): update shared toolchain and release standards 0.26.1

[davidvornholt]

Before. Standards consumers inherit Biome 2.5.11 and shared Playwright 1.62.1, missing current fixes and lint rules. Bun types and the CLI's YAML parser also lag their latest releases.

Now. Upgrade Biome to 2.5.13, both shared Playwright packages to 1.63.0, Bun types to 1.4.2, and YAML to 2.9.1. Release standards CLI 0.26.1 and align template pins, schema URLs, the Nix runtime dependency hash, and adoption examples.

Implementation

The strict nursery group enables the new rules automatically. noBunModules excludes only the existing Bun test and helper paths, where Bun imports are required; a regression fixture proves application imports remain rejected. The centralized Biome hold stays in place so consumers receive coordinated upgrades.

Supersedes dependency updates in #338, #339, and #340.

Verification

Completed checks

• bun run check:fix: passed all 9 tasks, including 1,404 CLI tests, shared-package tests, type checks, and lint.
• bun outdated --recursive: no outdated dependencies.
• git diff --check: passed.
• nix flake check: passed locally on x86_64-linux and in CI on both x86_64-linux and aarch64-linux, including the CLI package build and smoke checks.
• PaperSync consumer: all 25 quality tasks passed with the updated shared toolchain, including desktop and mobile browser checks.
• The first gate run identified Bun test imports under the new rule; the documented runtime exception and regression test resolve that failure.
• The first CI Nix builds found the stale YAML dependency hash on both architectures. Updated it to the identical hash computed by both runners; the local Nix gate now passes.