as shown in this document:
https://www.bluetooth.com/wp-content/uploads/Files/Specification/HTML/Core-54/out/en/host/attribute-protocol--att-.html and Zephyr's att.h, 0x0d should be 'invalid length' and 0x13 should be 'value not allowed':
#define BT_ATT_ERR_INVALID_ATTRIBUTE_LEN 0x0d
#define BT_ATT_ERR_UNLIKELY 0x0e
#define BT_ATT_ERR_INSUFFICIENT_ENCRYPTION 0x0f
#define BT_ATT_ERR_UNSUPPORTED_GROUP_TYPE 0x10
#define BT_ATT_ERR_INSUFFICIENT_RESOURCES 0x11
#define BT_ATT_ERR_DB_OUT_OF_SYNC 0x12
#define BT_ATT_ERR_VALUE_NOT_ALLOWED 0x13
while nrfConnect correctly identifies 0x0d, it shows 'unknown GATT service' for 0x13 (see image)

Thank you