Public scoreboard stopwatch feature

#10

db/migrate/20251209073711_add_start_time_to_contest.rb

@@ -0,0 +1,5 @@
+class AddStartTimeToContest < ActiveRecord::Migration[8.0]
+  def change
+    add_column :contests, :start_time, :datetime
+  end
+end

db/migrate/20251209075739_add_pause_time_to_contest.rb

@@ -0,0 +1,5 @@
+class AddPauseTimeToContest < ActiveRecord::Migration[8.0]
+  def change
+    add_column :contests, :pause_time, :datetime
+  end
+end

db/migrate/20251209081941_add_show_stopwatch_to_contest.rb

@@ -0,0 +1,5 @@
+class AddShowStopwatchToContest < ActiveRecord::Migration[8.0]
+  def change
+    add_column :contests, :show_stopwatch, :boolean
+  end
+end