Refactor document handling to JSON envelope

The `document.md` file has been replaced by `document.json`. This new
format acts as a JSON envelope, containing the original markdown content
along with metadata such as `covered_mtime`, `written_at`, and
`backend_id`.

This change addresses a bug where new recordings arriving during an LLM
analysis call could be ignored. The `covered_mtime` field in the new
JSON envelope ensures that the document's metadata accurately reflects
the state of recordings at the time of analysis, preventing incorrect
"analysis current" states.

Additionally, the `analysis_input.json` file is now removed upon
successful analysis, and a failure marker is used to indicate analysis
failures. This ensures that a case is re-analyzed if necessary.

The `analysis_idle_threshold_secs` configuration option has been
introduced to control the delay before a case in the `Required` state is
automatically promoted to `Idle` and enqueued for LLM analysis.

server/tests/common/mod.rs

@@ -25,7 +25,10 @@ pub mod session;
 pub mod users;
 
 // Re-exports for ergonomic `use common::*;` in most test files.
-pub use artefacts::{ANALYSIS_INPUT_FILE, CLOSE_MARKER, DOCUMENT_FILE, ONELINER_FILENAME};
+pub use artefacts::{
+    ANALYSIS_INPUT_FILE, CLOSE_MARKER, DOCUMENT_FILE, Document, ONELINER_FILENAME,
+    write_document_for_test,
+};
 pub use config::{TestConfig, unique_tmpdir};
 pub use doctate_common::Transcript;
 pub use http::{