fix: honor req_llm load_dotenv when starting llm_db

[mikehostetler]

Summary

• make req_llm own llm_db startup so it can set the default dotenv behavior before llm_db starts
• propagate config :req_llm, load_dotenv: false to llm_db unless :llm_db has its own explicit load_dotenv config
• add regressions for the issue [Bug]: Environment variables clobbered [redux] #527 startup path, existing env preservation, and explicit :llm_db override behavior

Testing

• mix format --check-formatted
• MIX_ENV=test mix compile --warnings-as-errors
• MIX_ENV=test mix test test/req_llm/application_test.exs
• MIX_ENV=test mix test

Closes #527