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. The backend logs its name, version and architecture once at
start, through the logger's Identify, which nothing called before.

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, HealthcheckResponse and
Healthcheck(). Its path, content type, status and code are unchanged.

Model: opus-5-5

backend/internal/handlers/healthcheck.go

@@ -6,6 +6,6 @@ import "net/http"
 // endpoint.
 func (s *Handlers) HandleHealthCheck() http.HandlerFunc {
 	return func(w http.ResponseWriter, r *http.Request) {
-		s.respondJSON(w, r, s.hc.Check(), http.StatusOK)
+		s.respondJSON(w, r, s.hc.Healthcheck(), http.StatusOK)
 	}
 }