feat(telegram): localized /start welcome with channel & chat follow links

The main bot answered /start with a single English line ("Tap to open Scrabble.").
Localize it: Russian or English by the sender's reported Telegram language
(Message.from.language_code, which the Bot API carries on the message itself — there is
no separate user-update event — English fallback), with the longer welcome copy and a
localized launch button ("Открыть «Эрудит»" / "Open “Erudite”").

The welcome links the game channel and the discussion chat by their public @username,
resolved once at startup from the configured TELEGRAM_GAME_CHANNEL_ID / TELEGRAM_CHAT_ID
via getChat and cached. A handle that is unset, private, or unreadable degrades to a
generic noun ("the channel" / "our chat") rather than a dangling "@", so the paragraph
always reads cleanly (the bot's info screen still lists the real links). Adds
GameChannelID to bot.Config (wired from the existing config) for the channel handle.

Tests: startText localization + handle embedding + per-slot generic fallback; handleStart
language selection; resolveWelcomeHandles. README updated.

platform/telegram/internal/bot/bot.go

@@ -33,8 +33,12 @@ type Config struct {
 	SendRatePerSecond int
 	// ChatID is the moderated discussion chat the bot gates write access in; 0
 	// disables chat gating (and the chat_member long-poll subscription). Gating needs
-	// the bot to be an administrator there with the restrict-members right.
+	// the bot to be an administrator there with the restrict-members right. Its public
+	// @username is also resolved at startup for the /start welcome's discussion link.
 	ChatID int64
+	// GameChannelID is the game channel whose public @username the /start welcome links
+	// to (resolved from this id via getChat at startup); 0 omits that follow link.
+	GameChannelID int64
 }
 
 // EligibilityResolver answers whether the Telegram user identified by externalID
@@ -54,6 +58,13 @@ type Bot struct {
 	limiter *rate.Limiter
 	// chatID is the moderated discussion chat (0 disables gating).
 	chatID int64
+	// channelID is the game channel (0 omits its welcome follow link).
+	channelID int64
+	// channelUsername and chatUsername are the public @usernames (without the leading
+	// @) of the game channel and the discussion chat, resolved once at startup
+	// (resolveWelcomeHandles) for the /start welcome's follow links; "" when unresolved.
+	channelUsername string
+	chatUsername    string
 	// botID is the bot's own Telegram user id (resolved at startup); it skips the
 	// chat_member updates the bot's own restrict actions generate — the grant loop guard.
 	botID int64
@@ -69,7 +80,7 @@ func New(cfg Config, log *zap.Logger) (*Bot, error) {
 	if log == nil {
 		log = zap.NewNop()
 	}
-	t := &Bot{miniAppURL: cfg.MiniAppURL, log: log, chatID: cfg.ChatID}
+	t := &Bot{miniAppURL: cfg.MiniAppURL, log: log, chatID: cfg.ChatID, channelID: cfg.GameChannelID}
 	if cfg.SendRatePerSecond > 0 {
 		t.limiter = rate.NewLimiter(rate.Limit(cfg.SendRatePerSecond), cfg.SendRatePerSecond)
 	}
@@ -123,9 +134,43 @@ func (t *Bot) Run(ctx context.Context) {
 	if t.chatID != 0 {
 		t.logChatAdminStatus(ctx)
 	}
+	t.resolveWelcomeHandles(ctx)
 	t.api.Start(ctx)
 }
 
+// resolveWelcomeHandles resolves, once at startup, the public @usernames of the game
+// channel and the discussion chat from their configured ids (getChat), caching them for
+// the /start welcome's follow links. It runs before the update loop, so the handles are
+// set before any /start is handled; a chat that is unset, private (no public username)
+// or unreadable simply leaves its handle empty and the welcome omits that follow link.
+func (t *Bot) resolveWelcomeHandles(ctx context.Context) {
+	t.channelUsername = t.resolveUsername(ctx, t.channelID, "game channel")
+	t.chatUsername = t.resolveUsername(ctx, t.chatID, "discussion chat")
+}
+
+// resolveUsername returns the public @username (without the leading @) of the chat with
+// the given id, or "" when id is 0, the chat has no public username, or getChat fails —
+// logging the reason, since a missing handle silently drops a welcome follow link.
+func (t *Bot) resolveUsername(ctx context.Context, id int64, label string) string {
+	if id == 0 {
+		return ""
+	}
+	chat, err := t.api.GetChat(ctx, &tgbot.GetChatParams{ChatID: id})
+	if err != nil {
+		t.log.Warn("welcome: getChat failed; follow link omitted",
+			zap.String("chat", label), zap.Int64("id", id), zap.Error(err))
+		return ""
+	}
+	if chat.Username == "" {
+		t.log.Warn("welcome: chat has no public @username; follow link omitted",
+			zap.String("chat", label), zap.Int64("id", id))
+		return ""
+	}
+	t.log.Info("welcome: resolved follow link",
+		zap.String("chat", label), zap.String("username", chat.Username))
+	return chat.Username
+}
+
 // logChatAdminStatus checks, at startup, whether the bot can actually gate the
 // moderated chat — it must be an administrator there with the restrict-members
 // ("Ban users") right, or Telegram delivers no chat_member updates and restricts
@@ -198,11 +243,19 @@ func (t *Bot) handleStart(ctx context.Context, api *tgbot.Bot, update *models.Up
 	if update.Message.Chat.Type != models.ChatTypePrivate {
 		return
 	}
+	// The sender's Telegram language rides on the message itself (Message.from.language_code
+	// in the Bot API — there is no separate user-update event); fall back to English when it
+	// is absent.
+	lang := ""
+	if update.Message.From != nil {
+		lang = update.Message.From.LanguageCode
+	}
+	text, button := startText(lang, t.channelUsername, t.chatUsername)
 	startParam := startPayload(update.Message.Text)
 	if _, err := api.SendMessage(ctx, &tgbot.SendMessageParams{
 		ChatID:      update.Message.Chat.ID,
-		Text:        "Tap to open Scrabble.",
-		ReplyMarkup: t.launchMarkup("Open Scrabble", startParam),
+		Text:        text,
+		ReplyMarkup: t.launchMarkup(button, startParam),
 	}); err != nil {
 		t.log.Warn("reply to start failed", zap.Error(err))
 	}