Hello,
I just tested myself and everything worked as expected.
I suggest checking if you have enabled SMS rules:
Also, are you sure your SIM card plan allows you to send and receive messages?
Then check if your SMS syntax is correct, it should be like that to get status message:
yourrouterpassword status
Regarding your question about SMS log, it shows only general messages that do not have any router special commands like the one above.
Regards.