fix: resolve LSP serializer options

Configure the sidecar LSP tool serializer with a DefaultJsonTypeInfoResolver and freeze it read-only before handing it to AIFunctionFactory. Add regression coverage so enabling LSP-backed tools cannot reintroduce the runtime JsonSerializerOptions failure.

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

sidecar/tests/Eryx.AgentHost.Tests/LspToolSessionTests.cs

@@ -0,0 +1,27 @@
+using System.Text.Json;
+using Eryx.AgentHost.Services;
+
+namespace Eryx.AgentHost.Tests;
+
+public sealed class LspToolSessionTests
+{
+    [Fact]
+    public void CreateJsonSerializerOptions_ReturnsReadOnlyResolverBackedOptions()
+    {
+        JsonSerializerOptions options = LspToolSession.CreateJsonSerializerOptions();
+
+        Assert.True(options.IsReadOnly);
+        Assert.NotNull(options.TypeInfoResolver);
+
+        string json = JsonSerializer.Serialize(
+            new
+            {
+                RelativePath = "src/file.ts",
+                Line = 12,
+                Character = 4,
+            },
+            options);
+
+        Assert.Contains("relativePath", json);
+    }
+}