feat(race): add contest countdown timer

Add race.lua with a 1-second vim.uv timer that counts down to a contest
start time and auto-calls setup.setup_contest() at T=0. Exposes
M.start(), M.stop(), and M.status() for command dispatch and statusline
integration.

lua/cp/race.lua

@@ -0,0 +1,143 @@
+local M = {}
+
+local cache = require('cp.cache')
+local constants = require('cp.constants')
+local logger = require('cp.log')
+local scraper = require('cp.scraper')
+
+local race_state = {
+  timer = nil,
+  platform = nil,
+  contest_id = nil,
+  language = nil,
+  start_time = nil,
+}
+
+local function format_countdown(seconds)
+  local h = math.floor(seconds / 3600)
+  local m = math.floor((seconds % 3600) / 60)
+  local s = seconds % 60
+  return string.format('%02d:%02d:%02d', h, m, s)
+end
+
+function M.start(platform, contest_id, language)
+  if not platform or not vim.tbl_contains(constants.PLATFORMS, platform) then
+    logger.log('Invalid platform', vim.log.levels.ERROR)
+    return
+  end
+  if not contest_id or contest_id == '' then
+    logger.log('Contest ID required', vim.log.levels.ERROR)
+    return
+  end
+  if race_state.timer then
+    logger.log('Race already active. Use :CP race stop first.', vim.log.levels.WARN)
+    return
+  end
+
+  cache.load()
+  local start_time = cache.get_contest_start_time(platform, contest_id)
+
+  if not start_time then
+    logger.log('Fetching contest list...', vim.log.levels.INFO, true)
+    local contests = scraper.scrape_contest_list(platform)
+    if contests and #contests > 0 then
+      cache.set_contest_summaries(platform, contests)
+      start_time = cache.get_contest_start_time(platform, contest_id)
+    end
+  end
+
+  if not start_time then
+    logger.log(
+      ('No start time found for %s contest %s'):format(
+        constants.PLATFORM_DISPLAY_NAMES[platform] or platform,
+        contest_id
+      ),
+      vim.log.levels.ERROR
+    )
+    return
+  end
+
+  local remaining = start_time - os.time()
+  if remaining <= 0 then
+    logger.log('Contest has already started, setting up...', vim.log.levels.INFO, true)
+    require('cp.setup').setup_contest(platform, contest_id, nil, language)
+    return
+  end
+
+  race_state.platform = platform
+  race_state.contest_id = contest_id
+  race_state.language = language
+  race_state.start_time = start_time
+
+  logger.log(
+    ('Race started for %s %s — %s remaining'):format(
+      constants.PLATFORM_DISPLAY_NAMES[platform] or platform,
+      contest_id,
+      format_countdown(remaining)
+    ),
+    vim.log.levels.INFO,
+    true
+  )
+
+  local timer = vim.uv.new_timer()
+  race_state.timer = timer
+  timer:start(
+    1000,
+    1000,
+    vim.schedule_wrap(function()
+      local r = race_state.start_time - os.time()
+      if r <= 0 then
+        timer:stop()
+        timer:close()
+        race_state.timer = nil
+        local p = race_state.platform
+        local c = race_state.contest_id
+        local l = race_state.language
+        race_state.platform = nil
+        race_state.contest_id = nil
+        race_state.language = nil
+        race_state.start_time = nil
+        logger.log('Contest started!', vim.log.levels.INFO, true)
+        require('cp.setup').setup_contest(p, c, nil, l)
+      else
+        vim.notify(
+          ('[cp.nvim] %s %s — %s'):format(
+            constants.PLATFORM_DISPLAY_NAMES[race_state.platform] or race_state.platform,
+            race_state.contest_id,
+            format_countdown(r)
+          ),
+          vim.log.levels.INFO
+        )
+      end
+    end)
+  )
+end
+
+function M.stop()
+  if not race_state.timer then
+    logger.log('No active race', vim.log.levels.WARN)
+    return
+  end
+  race_state.timer:stop()
+  race_state.timer:close()
+  race_state.timer = nil
+  race_state.platform = nil
+  race_state.contest_id = nil
+  race_state.language = nil
+  race_state.start_time = nil
+  logger.log('Race cancelled', vim.log.levels.INFO, true)
+end
+
+function M.status()
+  if not race_state.timer or not race_state.start_time then
+    return { active = false }
+  end
+  return {
+    active = true,
+    platform = race_state.platform,
+    contest_id = race_state.contest_id,
+    remaining_seconds = math.max(0, race_state.start_time - os.time()),
+  }
+end
+
+return M