They don't. Paragraph 4.2, "Customer's Ownership of Output" [0]. I recite verbatim below for the sake of clarity.
These are about processing the data, not owning it. They need to process the data eg to provide llm-based tab-completion. A completion is derivative work, and it is also owned by the customer, as it says below.
[0] https://zed.dev/terms#42-customers-ownership-of-output
> The Service may generate specifically for, and make available to, Customer text and written content based on or in response to Customer Data input into the Service (collectively, “Output”), including through the use of technologies that incorporate or rely upon artificial intelligence, machine learning techniques, and other similar technology and features. As between the Parties, to the greatest extent permitted by applicable Laws, Customer owns all Output and Zed hereby irrevocably assigns to Customer all right, title, and interest in and to the Output that Zed may possess. For the avoidance of doubt, Zed and its AI Providers will not retain or use Customer Data for the purpose of improving or training the Service or any AI Provider products, except to the extent Customer explicitly opts-in on Zed’s specific feature to allow training and/or such improvement (such as fine-tuning) and is solely for the benefit of Customer.