[test-improver] Improve tests for logger package (#5577)

## File Analyzed

- **Test Files**: `internal/logger/markdown_logger_test.go`,
`internal/logger/server_file_logger_test.go`
- **Package**: `internal/logger`

## Improvements Made

### Increased Coverage

Eight backward-compatibility wrapper functions had **0% coverage**.
These are one-liner delegates that forward calls to the canonical
`LogXxxToMarkdown` / `LogXxxToServer` functions. Adding tests for them
verifies the delegation chain works correctly and ensures future
refactors don't accidentally break the public API.

**Functions now covered:**
- ✅ `LogInfoMd` → `LogInfoToMarkdown`
- ✅ `LogWarnMd` → `LogWarnToMarkdown`
- ✅ `LogErrorMd` → `LogErrorToMarkdown`
- ✅ `LogDebugMd` → `LogDebugToMarkdown`
- ✅ `LogInfoWithServer` → `LogInfoToServer`
- ✅ `LogWarnWithServer` → `LogWarnToServer`
- ✅ `LogErrorWithServer` → `LogErrorToServer`
- ✅ `LogDebugWithServer` → `LogDebugToServer`

**Coverage improvement:**
- **Previous**: 96.1%
- **New**: 97.7%
- **Improvement**: +1.6%

### Test Design

Each new test:
1. Initialises a real logger in a `t.TempDir()` directory (no
side-effects on global state across test runs)
2. Calls all four level wrappers with a formatted message
3. Closes/flushes the logger so the file is written
4. Reads the log file and asserts each expected message is present

Tests follow the existing patterns in the file (bound asserters,
`require.NoError` for fatal errors, `assert.Contains` for content
checks).

## Test Execution

```
=== RUN   TestLogMdBackwardCompatWrappers
--- PASS: TestLogMdBackwardCompatWrappers (0.00s)
=== RUN   TestLogWithServerBackwardCompatWrappers
--- PASS: TestLogWithServerBackwardCompatWrappers (0.00s)
PASS
ok  github.com/github/gh-aw-mcpg/internal/logger  0.296s  coverage: 97.7% of statements
```

---
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Author: lpcox

internal/logger/markdown_logger_test.go

@@ -377,3 +377,31 @@ func TestGetEmojiForLevel(t *testing.T) {
 		})
 	}
 }
+
+// TestLogMdBackwardCompatWrappers verifies the backward-compatibility wrappers
+// (LogInfoMd, LogWarnMd, LogErrorMd, LogDebugMd) delegate to their canonical
+// counterparts and produce visible output in the markdown log file.
+func TestLogMdBackwardCompatWrappers(t *testing.T) {
+	tmpDir := t.TempDir()
+	logDir := filepath.Join(tmpDir, "md-logs")
+
+	err := InitMarkdownLogger(logDir, "gateway.md")
+	require.NoError(t, err)
+
+	LogInfoMd("test", "md compat info %s", "msg")
+	LogWarnMd("test", "md compat warn %s", "msg")
+	LogErrorMd("test", "md compat error %s", "msg")
+	LogDebugMd("test", "md compat debug %s", "msg")
+
+	err = CloseMarkdownLogger()
+	require.NoError(t, err)
+
+	content, err := os.ReadFile(filepath.Join(logDir, "gateway.md"))
+	require.NoError(t, err)
+
+	contentStr := string(content)
+	assert.Contains(t, contentStr, "md compat info msg", "LogInfoMd should write to markdown log")
+	assert.Contains(t, contentStr, "md compat warn msg", "LogWarnMd should write to markdown log")
+	assert.Contains(t, contentStr, "md compat error msg", "LogErrorMd should write to markdown log")
+	assert.Contains(t, contentStr, "md compat debug msg", "LogDebugMd should write to markdown log")
+}

internal/logger/server_file_logger_test.go

@@ -464,3 +464,33 @@ func TestServerFileLoggerGetOrCreate_FileCreationError(t *testing.T) {
 	sfl.mu.RUnlock()
 	assert.False(t, exists, "files map should not contain server1 after creation failure")
 }
+
+// TestLogWithServerBackwardCompatWrappers verifies the backward-compatibility wrappers
+// (LogInfoWithServer, LogWarnWithServer, LogErrorWithServer, LogDebugWithServer) delegate
+// to their canonical counterparts and produce visible output in the log file.
+func TestLogWithServerBackwardCompatWrappers(t *testing.T) {
+	tmpDir := t.TempDir()
+	logDir := filepath.Join(tmpDir, "server-logs")
+
+	err := InitServerFileLogger(logDir)
+	require.NoError(t, err)
+
+	serverID := "compat-server"
+
+	LogInfoWithServer(serverID, "test", "compat info %s", "msg")
+	LogWarnWithServer(serverID, "test", "compat warn %s", "msg")
+	LogErrorWithServer(serverID, "test", "compat error %s", "msg")
+	LogDebugWithServer(serverID, "test", "compat debug %s", "msg")
+
+	err = CloseServerFileLogger()
+	require.NoError(t, err)
+
+	content, err := os.ReadFile(filepath.Join(logDir, serverID+".log"))
+	require.NoError(t, err)
+
+	contentStr := string(content)
+	assert.Contains(t, contentStr, "compat info msg", "LogInfoWithServer should write to server log")
+	assert.Contains(t, contentStr, "compat warn msg", "LogWarnWithServer should write to server log")
+	assert.Contains(t, contentStr, "compat error msg", "LogErrorWithServer should write to server log")
+	assert.Contains(t, contentStr, "compat debug msg", "LogDebugWithServer should write to server log")
+}