[Feature] Adopt Biome as the repo formatter + linter

[pathosDev]

Rationale

The repo has no formatter or linter config. Several ticketed conventions need a lint host: #262 (fire-and-forget / floating-promise rule), #271 (null/undefined discipline), and the planned ban on raw timers in tests. Biome is a single fast binary providing formatter + linter in one, works well in a Bun-first repo, and is a devDependency only (dependency-policy conform) — avoiding the ESLint+Prettier+typescript-eslint multi-package matrix.

Scope

• biome.json with formatting + recommended lint rules.
• One mechanical format commit (no semantic changes), then enable targeted rules incrementally: floating promises ([Feature] Replace void unused-result with explicit fire-and-forget comment + lint rule #262), null/undefined ([Feature] Null/undefined disambiguation rule enforced via lint #271), no raw setTimeout/Bun.sleep in tests/ (pairs with the awaitCondition helper issue).
• CI check via biome ci.

Documentation

• CONTRIBUTING: format-on-save setup, commands.

Acceptance

• biome ci green in CI; the format commit keeps bun run typecheck + bun test green.

Relates

Improvement program M1 (foundation). #262, #271, #258.