Fix credential caching for index roots when URL ends in simple/ (#11336)

Closes https://github.com/astral-sh/uv/issues/11244

See test failure at
https://github.com/astral-sh/uv/pull/11336/commits/e12f98a3e40ddb61edd2fd32be4bfcf01c160102

crates/uv-distribution-types/src/index.rs

@@ -160,14 +160,19 @@ impl Index {
     /// For indexes with a `/simple` endpoint, this is simply the URL with the final segment
     /// removed. This is useful, e.g., for credential propagation to other endpoints on the index.
     pub fn root_url(&self) -> Option<Url> {
-        let segments = self.raw_url().path_segments()?;
-        let last = segments.last()?;
+        let mut segments = self.raw_url().path_segments()?;
+        let last = match segments.next_back()? {
+            // If the last segment is empty due to a trailing `/`, skip it (as in `pop_if_empty`)
+            "" => segments.next_back()?,
+            segment => segment,
+        };
+
         if !last.eq_ignore_ascii_case("simple") {
             return None;
         }
 
         let mut url = self.raw_url().clone();
-        url.path_segments_mut().ok()?.pop();
+        url.path_segments_mut().ok()?.pop_if_empty().pop();
         Some(url)
     }
 

crates/uv/tests/it/lock.rs

@@ -8358,6 +8358,52 @@ fn lock_multiple_indexes_same_realm_different_credentials() -> Result<()> {
     Ok(())
 }
 
+// Same as [`lock_multiple_indexes_same_realm_different_credentials`], but with trailing slashes
+// on the index URL
+#[test]
+fn lock_multiple_indexes_same_realm_different_credentials_trailing_slash() -> Result<()> {
+    let context = TestContext::new("3.12");
+
+    let pyproject_toml = context.temp_dir.child("pyproject.toml");
+    pyproject_toml.write_str(
+        r#"
+        [project]
+        name = "foo"
+        version = "0.1.0"
+        requires-python = ">=3.12"
+        dependencies = ["iniconfig", "anyio"]
+
+        [tool.uv.sources]
+        iniconfig = { index = "internal-proxy-heron" }
+        anyio = { index = "internal-proxy-eagle" }
+
+        [[tool.uv.index]]
+        name = "internal-proxy-heron"
+        url = "https://pypi-proxy.fly.dev/basic-auth-heron/simple/"
+
+        [[tool.uv.index]]
+        name = "internal-proxy-eagle"
+        url = "https://pypi-proxy.fly.dev/basic-auth-eagle/simple/"
+        "#,
+    )?;
+
+    // Provide credentials via environment variables.
+    uv_snapshot!(context.filters(), context.lock()
+        .env(EnvVars::index_username("INTERNAL_PROXY_HERON"), "public")
+        .env(EnvVars::index_password("INTERNAL_PROXY_HERON"), "heron")
+        .env(EnvVars::index_username("INTERNAL_PROXY_EAGLE"), "public")
+        .env(EnvVars::index_password("INTERNAL_PROXY_EAGLE"), "eagle"), @r###"
+    success: true
+    exit_code: 0
+    ----- stdout -----
+
+    ----- stderr -----
+    Resolved 5 packages in [TIME]
+    "###);
+
+    Ok(())
+}
+
 /// Resolve against an index that uses relative links.
 #[test]
 fn lock_relative_index() -> Result<()> {