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 -
Golden Contribution - Winter Update 2024 contestNovember 24, 2024
Brighid Grand Explorateur - Applying to TibiaQA team as ModeratorNovember 19, 2024
Looking for new TibiaQA staff membersJuly 12, 2024