Valve has confirmed that the UI from Steam Deck will replace Big Picture mode on Steam.
This was discovered after Valve employee austinp_valve responded to a question in the Steam Big Picture forum about the future of the interface.
Big Picture was released in 2012 as a console-like interface for users who plugged their PCs into large monitors and TVs while using a controller as opposed to keyboard and mouse. It became the basis for SteamOS which was used for the ill-fated Steam Machines.
It has seen very minimal updates since and is regarded by users as looking very outdated today. With the announcement of the Steam Deck, Valve has been working on a new version of SteamOS, which will bring a much needed UI refresh to many of Steam's aging components.