Log fx through slog, snake_case health check keys (closes #27)

fx wrote its own steps of starting and stopping as plain text to
stderr. It now logs them with its own slog event logger through the
backend's logger, so off a terminal every line from start to stop is
JSON. A config file that is found but cannot be read now makes
config.New return the error instead of panicking. A test runs the
server as a child process and checks that all it writes is JSON, on a
normal start and stop and with such a config file. The backend logs
its name, version and architecture once at start.

The health check's uptime keys are now uptime_seconds and
uptime_human, and its type and method take the names
GO_HTTP_SERVER_CONVENTIONS.md gives. Its path, content type, status
and code are unchanged.

Model: opus-5-5

TODO.md

@@ -23,6 +23,17 @@ latest run passes.
 
 # Completed Steps
 
+- 2026-10-03: the backend's logs are one stream (issue #27): fx logs its own
+  steps of starting and stopping through the backend's logger, so off a terminal
+  every line from start to stop is JSON, where fx used to write plain text to
+  stderr. A config file that is found but cannot be read now stops the start
+  with its error, logged as JSON like a bad setting, where it used to end in a
+  Go panic. A test runs the server as a child process and checks both. The
+  backend logs its name, version and architecture once at start. The health
+  check's uptime keys are now `uptime_seconds` and `uptime_human`; its path,
+  content type, `"status":"ok"` and 200 are unchanged. `SENTRY_DSN`,
+  `METRICS_USERNAME` and `METRICS_PASSWORD` are still read and still unused, and
+  left out of `backend/README.md`, until issues #94 and #95 wire them up
 - 2026-10-03: the frontend has a real linter (issue #47, and item 2 of issue
   #28): `eslint` with its recommended rules, set in `eslint.config.js`, runs in
   a new `frontend-lint` stage of `Dockerfile`, which the frontend stage waits