extension: Add debug_adapters to extension manifest (#30676)

Also pass worktree to the get_dap_binary.

Release Notes:

- N/A

crates/zed/Cargo.toml

@@ -45,6 +45,7 @@ dap_adapters.workspace = true
 debugger_ui.workspace = true
 debugger_tools.workspace = true
 db.workspace = true
+debug_adapter_extension.workspace = true
 diagnostics.workspace = true
 editor.workspace = true
 env_logger.workspace = true

crates/zed/src/main.rs

@@ -419,6 +419,7 @@ fn main() {
         .detach();
         let node_runtime = NodeRuntime::new(client.http_client(), Some(shell_env_loaded_rx), rx);
 
+        debug_adapter_extension::init(extension_host_proxy.clone(), cx);
         language::init(cx);
         language_extension::init(extension_host_proxy.clone(), languages.clone());
         languages::init(languages.clone(), node_runtime.clone(), cx);