zlog: Replace usages of env_logger in tests with zlog (#31436)

Also fixes:
https://github.com/zed-industries/zed/pull/31400#issuecomment-2908165249

Release Notes:

- N/A *or* Added/Fixed/Improved ...

crates/lsp/Cargo.toml

@@ -36,6 +36,6 @@ workspace-hack.workspace = true
 [dev-dependencies]
 async-pipe.workspace = true
 ctor.workspace = true
-env_logger.workspace = true
 gpui = { workspace = true, features = ["test-support"] }
 util = { workspace = true, features = ["test-support"] }
+zlog.workspace = true

crates/lsp/src/lsp.rs

@@ -1668,9 +1668,7 @@ mod tests {
 
     #[ctor::ctor]
     fn init_logger() {
-        if std::env::var("RUST_LOG").is_ok() {
-            env_logger::init();
-        }
+        zlog::init_test();
     }
 
     #[gpui::test]