It depends on `image` which in turn depends on a number of crates to handle different file types. If you disable all `image` features, it only has like 5 dependencies left.
It is also important to note that this is not specific to Zed. As someone else have mentioned, it is a cultural problem. I picked Zed as an example because that is what I compiled the last time, but it is definitely not limited to Zed. There are many Rust projects that pull in over 1000 dependencies and they do much less than Zed.