No, you do not have to be premium to sell or buy characters on Char Bazaar. -Official CM Reply
When you go to sell your character in-game it will let you know if you meet all the requirements by going to the Store and then clicking the button to sell your character which I highlighted in yellow. If you hover over the icon it will let you know it's to sell your character.
Here are additional sources about Character Auctions I recommend you read -
Loqhakk - Applying to TibiaQA team as ModeratorJuly 26, 2024
Nareull - Applying to TibiaQA team as ModeratorJuly 14, 2024
Looking for new TibiaQA staff membersJuly 12, 2024