You are free to use CC-BY-SA 3.0 in CC-BY-SA 4.0 work.  In other words:
- you can use SE content in your own 4.0 work
- SE can change the license to 4.0 at will
However, you cannot use 4.0 content in a 3.0 work. In other words, until SE updates the license, you cannot paste 4.0 content into a question/answer.
So, for your own reuse purposes, SE does not need to update the license. For SE reuse purposes, SE does need to update the license, just like they when updated from 2.5 to 3.0.
 This has been true since CC-BY-SA 2.0:
Version 2.0 licenses that feature the Share Alike requirement now clarify that derivatives may be re-published under one of three types of licenses: (1) the exact same license as the original work; (2) a later version of the same license as the original work; (3) an iCommons license that contains the same license elements as the original work (e.g. BY-SA-NC, as defined in Section 1 of each license). The version 1.0 licenses required that derivative be published under the exact same license only. Our tweak means much better compatibility across future jurisdiction-specific licenses and, going forward, across versions. Less forking, more fun. (See Section 4b.)
(from "Share Alike Across Borders" in Announcing (and explaining) our new 2.0 licenses)
Alternatively, follow the "More info" link that appears in the "same license" tooltip on the CC-BY-SA 3.0 human readable license.