Currently JsonLinesParser::from_line is called for both stdout and
stderr, so trait implementers cannot distinguish stdout and stderr.
Define a separate JsonLinesParser::from_stderr_line to make the
stdout/stderr distinction explicit, and update use sites. This is not
a behaviour change.
AI disclosure: Partially written by Codex and GPT-5.5.

Previously we read both stdout and stderr in the discover
protocol. Depending on the tool generating rust-project JSON, this
meant that a single stderr log message could break discovery.
Instead, only look for JSON from the discover command's stdout, and
forward stderr to the rust-analyzer logs.
Update both the implementation and the discover protocol docs to
reflect this behaviour.
AI disclosure: Code partly written by GPT-5.5.