docs: bind manual acceptance to the E2E database

[NoctilumeDev]

Purpose

The acceptance checklist initializes dark_room_library_e2e but did not direct the backend to that database. Add an explicit DB_URL example, explain that it belongs in the actual backend launch environment, and move demo-login verification after startup.

Impact

Only docs/manual-acceptance-checklist.md changes. The example matches setup-e2e-database.ps1 defaults, and explains how to match custom host, port, database and credentials. Revert this commit to restore the prior instructions.

Verification

• node scripts/check-doc-links.mjs: passed.
• PowerShell parser accepted the documented DB_URL assignment.
• Compared the documented JDBC prefix with the initialization script's parsed HostName, Port and DatabaseName defaults: matched.
• Compared the environment variable and JDBC options with application.yml.
• git diff --check: passed.
• No database reset, initialization or runtime acceptance experiment was executed locally.

Checklist

• Documentation correction stays within the maintenance scope.
• Application code, configuration defaults, SQL and runtime scripts are preserved.
• No new runtime behavior requires regression tests.
• No credentials, private data, proxy settings or machine-specific paths were added.