Upon taking the Oath of (higher federal) Office her California Senate seat became unfilled. A Vice President is also responsible for breaking tie votes - which wouldn’t be possible if she held both positions simultaneously.
I could be wrong.
She took the VP oath on January 20, 2021. Though she could have resigned her Senate seat early, I found a roll call Senate vote on whether to sustain a challenge to the electors from Pennsylvania from early in the morning of January 7 (https://www.senate.gov/legislative/LIS/roll_call_votes/vote1171/vote_117_1_00002.htm?congress=117&session=1&vote=00002). Harris voted Nay....