Start the local-auth E2E server with the running Bun

The local-auth test spawned its server through mise, which exists on
developer machines but not on the CI runner, so every attempt failed
with "Executable not found in $PATH: mise". Spawn process.execPath
instead, and skip process-group cleanup for a child that never started
so a spawn failure reports its real cause.

Assistant-model: Claude Opus 5.5
Assistant-workflow: inline
Assistant-verification: Playwright E2E passed: CI=1 bun run e2e e2e/local-auth.e2e.ts with Bun 1.3.2 and no mise on PATH (1/1)
Assistant-verification: bun run ci passed: dprint, oxlint, tokens
Assistant-verification: bun run types passed: all workspaces and E2E
Assistant-verification: bun test passed: 1566 pass, 2 PostgreSQL skips, 0 fail
Co-authored-by: Alex Lavaee <lavaman131@github.com>