Use full section paths for client registrations

[kzu]

Summary

• register client factories and chat clients under the full configuration section path
• keep optional id values as secondary lookup aliases
• remove ServiceKey and dotted registration aliases
• update docs and tests for the new lookup behavior

Validation

• dotnet build
• dnx --yes retest
• dotnet format whitespace -v:diag --exclude ~/.nuget
• dotnet format style -v:diag --exclude ~/.nuget

[kzu]

🧪 Details on Ubuntu 24.04.4 LTS

from retest v1.1.0 on .NET 10.0.8 with 💜 by @devlooped