[ty] Add ty.inlayHints.variableTypes server option (#19780)

## Summary

This PR adds a new `ty.inlayHints.variableTypes` server setting to
configure ty to include / exclude inlay hints at variable position.

Currently, we only support inlay hints at this position so this option
basically translates to enabling / disabling inlay hints for now :)

The VS Code extension PR is
https://github.com/astral-sh/ty-vscode/pull/112.

closes: astral-sh/ty#472

## Test Plan

Add E2E tests.

crates/ty_server/tests/e2e/inlay_hints.rs

@@ -0,0 +1,38 @@
+use anyhow::Result;
+use lsp_types::{Position, Range, notification::PublishDiagnostics};
+use ruff_db::system::SystemPath;
+use ty_server::ClientOptions;
+
+use crate::TestServerBuilder;
+
+/// Tests that disabling variable types inlay hints works correctly.
+#[test]
+fn variable_inlay_hints_disabled() -> Result<()> {
+    let workspace_root = SystemPath::new("src");
+    let foo = SystemPath::new("src/foo.py");
+    let foo_content = "x = 1";
+
+    let mut server = TestServerBuilder::new()?
+        .with_initialization_options(
+            ClientOptions::default().with_variable_types_inlay_hints(false),
+        )
+        .with_workspace(workspace_root, None)?
+        .with_file(foo, foo_content)?
+        .enable_inlay_hints(true)
+        .build()?
+        .wait_until_workspaces_are_initialized()?;
+
+    server.open_text_document(foo, &foo_content, 1);
+    let _ = server.await_notification::<PublishDiagnostics>()?;
+
+    let hints = server
+        .inlay_hints_request(foo, Range::new(Position::new(0, 0), Position::new(0, 5)))?
+        .unwrap();
+
+    assert!(
+        hints.is_empty(),
+        "Expected no inlay hints, but found: {hints:?}"
+    );
+
+    Ok(())
+}

crates/ty_server/tests/e2e/main.rs

@@ -28,6 +28,7 @@
 //! [`await_notification`]: TestServer::await_notification
 
 mod initialize;
+mod inlay_hints;
 mod publish_diagnostics;
 mod pull_diagnostics;
 
@@ -48,20 +49,21 @@ use lsp_types::notification::{
     Initialized, Notification,
 };
 use lsp_types::request::{
-    DocumentDiagnosticRequest, HoverRequest, Initialize, Request, Shutdown, WorkspaceConfiguration,
-    WorkspaceDiagnosticRequest,
+    DocumentDiagnosticRequest, HoverRequest, Initialize, InlayHintRequest, Request, Shutdown,
+    WorkspaceConfiguration, WorkspaceDiagnosticRequest,
 };
 use lsp_types::{
     ClientCapabilities, ConfigurationParams, DiagnosticClientCapabilities,
     DidChangeTextDocumentParams, DidChangeWatchedFilesClientCapabilities,
     DidChangeWatchedFilesParams, DidCloseTextDocumentParams, DidOpenTextDocumentParams,
     DocumentDiagnosticParams, DocumentDiagnosticReportResult, FileEvent, Hover, HoverParams,
-    InitializeParams, InitializeResult, InitializedParams, NumberOrString, PartialResultParams,
-    Position, PreviousResultId, PublishDiagnosticsClientCapabilities,
-    TextDocumentClientCapabilities, TextDocumentContentChangeEvent, TextDocumentIdentifier,
-    TextDocumentItem, TextDocumentPositionParams, Url, VersionedTextDocumentIdentifier,
-    WorkDoneProgressParams, WorkspaceClientCapabilities, WorkspaceDiagnosticParams,
-    WorkspaceDiagnosticReportResult, WorkspaceFolder,
+    InitializeParams, InitializeResult, InitializedParams, InlayHint, InlayHintClientCapabilities,
+    InlayHintParams, NumberOrString, PartialResultParams, Position, PreviousResultId,
+    PublishDiagnosticsClientCapabilities, Range, TextDocumentClientCapabilities,
+    TextDocumentContentChangeEvent, TextDocumentIdentifier, TextDocumentItem,
+    TextDocumentPositionParams, Url, VersionedTextDocumentIdentifier, WorkDoneProgressParams,
+    WorkspaceClientCapabilities, WorkspaceDiagnosticParams, WorkspaceDiagnosticReportResult,
+    WorkspaceFolder,
 };
 use ruff_db::system::{OsSystem, SystemPath, SystemPathBuf, TestSystem};
 use rustc_hash::FxHashMap;
@@ -725,6 +727,23 @@ impl TestServer {
         let id = self.send_request::<HoverRequest>(params);
         self.await_response::<HoverRequest>(&id)
     }
+
+    /// Sends a `textDocument/inlayHint` request for the document at the given path and range.
+    pub(crate) fn inlay_hints_request(
+        &mut self,
+        path: impl AsRef<SystemPath>,
+        range: Range,
+    ) -> Result<Option<Vec<InlayHint>>> {
+        let params = InlayHintParams {
+            text_document: TextDocumentIdentifier {
+                uri: self.file_uri(path),
+            },
+            range,
+            work_done_progress_params: WorkDoneProgressParams::default(),
+        };
+        let id = self.send_request::<InlayHintRequest>(params);
+        self.await_response::<InlayHintRequest>(&id)
+    }
 }
 
 impl fmt::Debug for TestServer {
@@ -908,6 +927,19 @@ impl TestServerBuilder {
         self
     }
 
+    /// Enable or disable inlay hints capability
+    pub(crate) fn enable_inlay_hints(mut self, enabled: bool) -> Self {
+        self.client_capabilities
+            .text_document
+            .get_or_insert_default()
+            .inlay_hint = if enabled {
+            Some(InlayHintClientCapabilities::default())
+        } else {
+            None
+        };
+        self
+    }
+
     /// Enable or disable file watching capability
     #[expect(dead_code)]
     pub(crate) fn enable_did_change_watched_files(mut self, enabled: bool) -> Self {