You will also find furniture in build mode. Some of it can be bought for simoleons, other pieces need to be purchased with Simcash. You will have to pay extra in the form of special house coupons for more luxurious equipment pieces. Furniture is mainly used in events, where the sims interact with it.
The first option you can pick in build mode is "collections". There are 3 types that will pop up when you enter the menu: house objects, career, and hobby. In each of them, you will find a few collections to choose from. They often consist of a few pieces each and require having a sufficiently high experience or career level. These objects are designed to facilitate the development of stories.
In The Sims Mobile, there is also room for classic furniture arrangement. In the "buy" section, you can choose which room you want to purchase furniture for and pick the ideal style for the new additions. Some of these options can be unlocked by collecting souvenirs or by reaching higher experience levels.