test(studio): seven FaiLog cases + visibleForTesting path override

FaiLog used to compute its destination directly from HOME, which
made it impossible to test without scribbling on the operator's
real ~/.fai/logs/. Adds a static testPathOverride seam tagged
@visibleForTesting so the singleton can be redirected at a per-
test temp file.

The new test/fai_log_test.dart covers:

  - append() writes one JSON-shaped line per event
  - context field round-trips when supplied
  - tail() returns oldest-first
  - tail(maxLines:) caps and keeps the newest entries
  - rotation moves the previous log to .log.1 past 256 KiB
  - path getter honours the override
  - writes to an impossible path do not throw — best-effort
    contract that protects the UI from log-write failures

Production behaviour is unchanged: when the override is null
the path getter still computes from HOME/USERPROFILE.

Signed-off-by: flemming-it <stefan.a.flemming@googlemail.com>

lib/data/fai_log.dart

@@ -23,6 +23,7 @@ import 'dart:async';
 import 'dart:convert';
 import 'dart:io';
 
+import 'package:meta/meta.dart';
 import 'package:path/path.dart' as p;
 
 class FaiLog {
@@ -37,7 +38,15 @@ class FaiLog {
 
   static const int _rotateBytes = 256 * 1024;
 
+  /// Test seam. Set this in `setUp` to redirect the singleton at
+  /// a per-test temp file; reset to `null` in `tearDown`. Production
+  /// code never touches it — the default getter computes from HOME.
+  @visibleForTesting
+  static String? testPathOverride;
+
   String get _path {
+    final override = testPathOverride;
+    if (override != null) return override;
     final home =
         Platform.environment['HOME'] ??
         Platform.environment['USERPROFILE'] ??