feat: select school terms and smooth refractive Dock motion

mobile/lib/domain/app_snapshot.dart

@@ -2,6 +2,7 @@ import 'app_settings.dart';
 import 'course.dart';
 import 'semester.dart';
 import 'exam_schedule.dart';
+import 'school_term.dart';
 
 class ImportMetadata {
   const ImportMetadata({
@@ -20,16 +21,32 @@ class AppSnapshot {
     List<Course> courses = const [],
     this.importMetadata,
     this.examSchedule,
+    SchoolTerm? schoolTerm,
     this.calendarCleanupPending = false,
     Map<String, String> calendarEventIds = const {},
-  }) : courses = List.unmodifiable(courses),
+  }) : schoolTerm = schoolTerm ?? _legacyTerm(courses, examSchedule),
+       courses = List.unmodifiable(courses),
        calendarEventIds = Map.unmodifiable(calendarEventIds);
   final AppSettings settings;
   final List<Course> courses;
   final ImportMetadata? importMetadata;
   final ExamSchedule? examSchedule;
+  final SchoolTerm? schoolTerm;
   final Map<String, String> calendarEventIds;
   final bool calendarCleanupPending;
+  static SchoolTerm? _legacyTerm(List<Course> courses, ExamSchedule? exams) {
+    final ids = courses
+        .map(
+          (course) => RegExp(r'^uestc-(\d+)-').firstMatch(course.id)?.group(1),
+        )
+        .whereType<String>()
+        .toSet();
+    if (exams != null) ids.add(exams.termId);
+    if (ids.length != 1) return null;
+    final id = int.tryParse(ids.single);
+    return id != null && id >= 1 && id <= 9999 ? SchoolTerm(id) : null;
+  }
+
   AppSnapshot copyWith({
     AppSettings? settings,
     List<Course>? courses,
@@ -38,6 +55,7 @@ class AppSnapshot {
     bool clearMetadata = false,
     ExamSchedule? examSchedule,
     bool clearExams = false,
+    SchoolTerm? schoolTerm,
     bool? calendarCleanupPending,
   }) => AppSnapshot(
     settings: settings ?? this.settings,
@@ -46,6 +64,7 @@ class AppSnapshot {
         ? null
         : importMetadata ?? this.importMetadata,
     examSchedule: clearExams ? null : examSchedule ?? this.examSchedule,
+    schoolTerm: schoolTerm ?? this.schoolTerm,
     calendarEventIds: calendarEventIds ?? this.calendarEventIds,
     calendarCleanupPending:
         calendarCleanupPending ?? this.calendarCleanupPending,
@@ -53,6 +72,7 @@ class AppSnapshot {
   Map<String, dynamic> toJson() => {
     'schemaVersion': 1,
     'examSchedule': examSchedule?.toJson(),
+    'schoolTerm': schoolTerm?.toJson(),
     'courses': courses.map((c) => c.toJson()).toList(),
     'settings': {
       'semester': settings.semester == null
@@ -116,6 +136,11 @@ class AppSnapshot {
             );
       final metadata = json['importMetadata'];
       return AppSnapshot(
+        schoolTerm: json['schoolTerm'] == null
+            ? null
+            : SchoolTerm.fromJson(
+                Map<String, dynamic>.from(json['schoolTerm'] as Map),
+              ),
         examSchedule: json['examSchedule'] == null
             ? null
             : ExamSchedule.fromJson(