Avoid modify config during training.

As the title says, we should solve the conflicts within the configs among different algorithms before calling `client.run()` or `server.run()`.

Start by tracing configuration handling through the client.run() and server.run() entry points, including how different algorithms contribute conflicting settings. Determine where conflicts can be resolved before training begins and verify that training no longer modifies the configs; the issue names no files or tests, so identify the relevant coverage while investigating.

Written by the indexing model from the issue text.