Turn completion instructions were being injected as a system message in
the LLM context, which caused warning spam when system_instruction was
also set, did not persist across full context updates, and broke LLMs
that do not support consecutive system messages.
Instead, compose the turn completion instructions into the LLM service
system_instruction field. This is managed via _base_system_instruction
which stores the original value for restoration when turn completion is
disabled.
