Did Moderna CEO Suddenly Dump $400M in Stock?

In February 2022, a rumor started circulating online that Moderna CEO Stéphane Bancel had just “dumped $400 million in stock” and deleted his Twitter account. The conspiracy-mongering website Newspunch reported:
Moderna CEO Just Dumped $400 Million in Stock and Deleted His Twitter Account
Days after Pfizer admitted a safety audit could wipe billions off their stock market valuation, Moderna CEO Stéphane Bancel dumped hundreds of millions of dollars in stock and deleted his Twitter account.
This rumor was also circulated on social media.