zed_extension_api: Fork new version of extension API (#27390)

This PR forks a new version of the `zed_extension_api` in preparation
for new changes.

Release Notes:

- N/A

Cargo.lock

@@ -9621,7 +9621,7 @@ name = "perplexity"
 version = "0.1.0"
 dependencies = [
  "serde",
- "zed_extension_api 0.3.0",
+ "zed_extension_api 0.4.0",
 ]
 
 [[package]]
@@ -17423,7 +17423,7 @@ dependencies = [
 
 [[package]]
 name = "zed_extension_api"
-version = "0.3.0"
+version = "0.4.0"
 dependencies = [
  "serde",
  "serde_json",
@@ -17481,7 +17481,7 @@ dependencies = [
 name = "zed_test_extension"
 version = "0.1.0"
 dependencies = [
- "zed_extension_api 0.3.0",
+ "zed_extension_api 0.4.0",
 ]
 
 [[package]]