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 slog event logger through the
backend's logger, so off a terminal every line the backend's own
logger and fx write is JSON. A malformed config file 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; its type and method take the names
GO_HTTP_SERVER_CONVENTIONS.md gives.

Model: opus-5-5

TODO.md

@@ -23,6 +23,18 @@ 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 the backend's own logger and fx write 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