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/zlog/src/zlog.rs

@@ -5,18 +5,38 @@ mod env_config;
 pub mod filter;
 pub mod sink;
 
+use anyhow::Context;
 pub use sink::{flush, init_output_file, init_output_stdout};
 
 pub const SCOPE_DEPTH_MAX: usize = 4;
 
 pub fn init() {
-    process_env();
-    log::set_logger(&ZLOG).expect("Logger should not be initialized twice");
+    try_init().expect("Failed to initialize logger");
+}
+
+pub fn try_init() -> anyhow::Result<()> {
+    log::set_logger(&ZLOG).context("cannot be initialized twice")?;
     log::set_max_level(log::LevelFilter::max());
+    process_env();
+    Ok(())
+}
+
+pub fn init_test() {
+    if get_env_config().is_some() {
+        if try_init().is_ok() {
+            init_output_stdout();
+        }
+    }
+}
+
+fn get_env_config() -> Option<String> {
+    std::env::var("ZED_LOG")
+        .or_else(|_| std::env::var("RUST_LOG"))
+        .ok()
 }
 
 pub fn process_env() {
-    let Ok(env_config) = std::env::var("ZED_LOG").or_else(|_| std::env::var("RUST_LOG")) else {
+    let Some(env_config) = get_env_config() else {
         return;
     };
     match env_config::parse(&env_config) {