Answer
Open and read the qualifying chats to clear it. Opening Home or switching tabs alone does not mark messages as read. Read state syncs between devices and may take a moment; an offline device can show older information.
On updated builds, an unread chat’s More menu offers Mark as Read. It clears the messages and personal activity already observed without opening the conversation. A newer message stays unread, so if one arrives while saving, the chat simply stays unread. A connection problem is retried once; if saving still fails, the unread state returns and an error appears.
On phone layouts, an unread Chats shortcut can also appear at the left of the chat header. It opens the People list while preserving your draft. An unfinished voice recording still needs confirmation before leaving. The Home Chats tab remains available after everything is read.