Google Hangouts is no longer offer SMS supports unless you subscribe to Google Voice or Project Fi . You will not be able to find all your chats under one place but will have to use two separate applications. However, Google has not been very clear about a transition and migration.
The choices now available to you are returning to using the basic SMS messaging service or switching to Allo but you will lose the interest of centralizing SMS and other conversations. Facebook Messenger and signal remains a good way to combine different type of chat in place.
Anyway, giving SMS through Hangouts is completed. The email service of Google is steadily dropping interest, even when the application form must still endure sometime. The Mountain View company is unquestionably wanting to modify users.