No, it isn’t unusual that Kamala Harris is still in the Senate.

Source: https://www.nytimes.com/2020/12/01/technology/no-it-isnt-unusual-that-kamala-harris-is-still-in-the-senate.html
December 02, 2020 at 12:39AM

In the past half century, it has been common for vice president-elects to resign from their previous posts in late December or January.