Unify fallback and unimplemented API error handling

- Add a shared common error response schema and unknown error code for business-level fallbacks
- Return business error payloads for router NoRoute and NoMethod fallbacks
- Align the existing event list fallback response with the shared error structure
- Introduce an explicit unimplemented API error type instead of relying on formatted strings
- Make /api batch dispatch return per-item status 600 error entries for unimplemented modules and actions without failing the whole batch

Signed-off-by: Sean Du <do4suki@gmail.com>

internal/handler/api/live/live.go

@@ -1,7 +1,7 @@
 package live
 
 import (
-	"fmt"
+	honokautils "honoka-chan/internal/utils"
 
 	"github.com/gin-gonic/gin"
 )
@@ -13,7 +13,7 @@ func LiveApi(ctx *gin.Context, action string) (res any, err error) {
 	case "schedule":
 		res, err = liveSchedule(ctx)
 	default:
-		err = fmt.Errorf("unimplemented action: live: %s", action)
+		err = honokautils.NewUnimplementedActionError("live", action)
 	}
 	return res, err
 }