Real talk, in the event of the changing of a new kingdom's monarch, missives would first be sent to all neighbouring nations greeting them, introducing the new monarch and after that only seeking to establish diplomatic ties. Following the receipt of those missives, neighbouring kingdoms would seek to confirm that the new monarch is stable and has political support. THEN messages of congratulations follow. Then usually that's when you plan for envoys or embassies. Thank you for the plot hole, Kashiwa Ten.
Eta: NOT TO MENTION YOU ALWAYS SEND AN OFFICIAL LETTER IN ADVANCE SO THE KINGDOM YOU'RE VISITING WILL KNOW TO PREPARE FOR YOUR DELEGATION!!! THEY STILL EVEN DO THIS TODAY DESPITE THE EXISTENCE OF EMAIL!!!! DIPLOMACY 101 (I'm having a heart attack rn)