app-server: add JSON tracing logs (#12287)

- add `LOG_FORMAT=json` support for app-server tracing logs via
`tracing_subscriber`'s built-in JSON formatter
- keep the default human-readable format unchanged and keep `RUST_LOG`
filtering behavior
- document the env var and update lockfile

codex-rs/Cargo.lock

@@ -9530,6 +9530,16 @@ dependencies = [
  "web-time",
 ]
 
+[[package]]
+name = "tracing-serde"
+version = "0.2.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "704b1aeb7be0d0a84fc9828cae51dab5970fee5088f83d1dd7ee6f6246fc6ff1"
+dependencies = [
+ "serde",
+ "tracing-core",
+]
+
 [[package]]
 name = "tracing-subscriber"
 version = "0.3.22"
@@ -9540,12 +9550,15 @@ dependencies = [
  "nu-ansi-term",
  "once_cell",
  "regex-automata",
+ "serde",
+ "serde_json",
  "sharded-slab",
  "smallvec",
  "thread_local",
  "tracing",
  "tracing-core",
  "tracing-log",
+ "tracing-serde",
 ]
 
 [[package]]