botapi: getChatMemberCount, getChatMember, and a fuller getChat

- getChatMemberCount: channel/supergroup participant count (numeric chat_id).
- getChatMember: resolves a member via GetParticipant, projected to a Bot API
  ChatMember (creator/administrator/restricted/member/left/kicked with the
  matching rights); a user simply not in an accessible chat returns "left".
- getChat now uses the full channel view and adds permissions (from the default
  restrictions), slow_mode_delay, linked_chat_id and pinned_message.

Channel-only methods reject user chat_ids; private chats the bot cannot access
return CHAT_NOT_FOUND.

internal/botapi/projection.go

@@ -392,9 +392,127 @@ func apiChatFull(chat domain.BotAPIChat) map[string]any {
 	if chat.Fake {
 		out["is_fake"] = true
 	}
+	if chat.SlowModeDelay > 0 {
+		out["slow_mode_delay"] = chat.SlowModeDelay
+	}
+	if chat.LinkedChatID != 0 {
+		out["linked_chat_id"] = -1000000000000 - chat.LinkedChatID
+	}
+	if chat.Permissions != nil {
+		out["permissions"] = apiChatPermissions(*chat.Permissions)
+	}
+	if chat.PinnedMessage != nil {
+		out["pinned_message"] = apiMessage(*chat.PinnedMessage, chat.PinnedMessageUsers)
+	}
 	return out
 }
 
+// apiChatPermissions projects a channel's default restrictions as a Bot API
+// ChatPermissions object (a right is granted when the matching restriction is
+// off).
+func apiChatPermissions(b domain.ChannelBannedRights) map[string]any {
+	text := !b.SendMessages && !b.SendPlain
+	return map[string]any{
+		"can_send_messages":         text,
+		"can_send_audios":           !b.SendMedia && !b.SendAudios,
+		"can_send_documents":        !b.SendMedia && !b.SendDocs,
+		"can_send_photos":           !b.SendMedia && !b.SendPhotos,
+		"can_send_videos":           !b.SendMedia && !b.SendVideos,
+		"can_send_video_notes":      !b.SendMedia && !b.SendRoundvideos,
+		"can_send_voice_notes":      !b.SendMedia && !b.SendVoices,
+		"can_send_polls":            !b.SendPolls,
+		"can_send_other_messages":   !b.SendStickers && !b.SendGifs && !b.SendGames && !b.SendInline,
+		"can_add_web_page_previews": !b.EmbedLinks,
+		"can_change_info":           !b.ChangeInfo,
+		"can_invite_users":          !b.InviteUsers,
+		"can_pin_messages":          !b.PinMessages,
+		"can_manage_topics":         !b.ManageTopics,
+	}
+}
+
+// apiChatMember projects a resolved member as a Bot API ChatMember object.
+func apiChatMember(m domain.BotAPIChatMember) map[string]any {
+	out := map[string]any{
+		"status": botAPIMemberStatus(m.Member),
+		"user":   apiUser(userOrPlaceholder(m.User, m.Member.UserID)),
+	}
+	switch out["status"] {
+	case "creator":
+		if m.Member.AdminRights.Anonymous {
+			out["is_anonymous"] = true
+		}
+		if m.Member.Rank != "" {
+			out["custom_title"] = m.Member.Rank
+		}
+	case "administrator":
+		a := m.Member.AdminRights
+		out["can_be_edited"] = false
+		out["is_anonymous"] = a.Anonymous
+		out["can_manage_chat"] = a.ManageChat
+		out["can_delete_messages"] = a.DeleteMessages
+		out["can_manage_video_chats"] = a.ManageCall
+		out["can_restrict_members"] = a.BanUsers
+		out["can_promote_members"] = a.AddAdmins
+		out["can_change_info"] = a.ChangeInfo
+		out["can_invite_users"] = a.InviteUsers
+		out["can_post_messages"] = a.PostMessages
+		out["can_edit_messages"] = a.EditMessages
+		out["can_pin_messages"] = a.PinMessages
+		out["can_manage_topics"] = a.ManageTopics
+		out["can_post_stories"] = a.PostStories
+		out["can_edit_stories"] = a.EditStories
+		out["can_delete_stories"] = a.DeleteStories
+		if m.Member.Rank != "" {
+			out["custom_title"] = m.Member.Rank
+		}
+	case "restricted":
+		b := m.Member.BannedRights
+		out["is_member"] = m.Member.Status == domain.ChannelMemberActive
+		for k, v := range apiChatPermissions(b) {
+			out[k] = v
+		}
+		if b.UntilDate > 0 {
+			out["until_date"] = b.UntilDate
+		}
+	case "kicked":
+		if m.Member.BannedRights.UntilDate > 0 {
+			out["until_date"] = m.Member.BannedRights.UntilDate
+		}
+	}
+	return out
+}
+
+func userOrPlaceholder(u domain.User, id int64) domain.User {
+	if u.ID != 0 {
+		return u
+	}
+	return domain.User{ID: id}
+}
+
+func botAPIMemberStatus(m domain.ChannelMember) string {
+	switch {
+	case m.Role == domain.ChannelRoleCreator:
+		return "creator"
+	case m.Status == domain.ChannelMemberKicked, m.Status == domain.ChannelMemberBanned, m.BannedRights.ViewMessages:
+		return "kicked"
+	case m.Role == domain.ChannelRoleAdmin:
+		return "administrator"
+	case m.Status == domain.ChannelMemberLeft:
+		return "left"
+	case botAPIMemberRestricted(m.BannedRights):
+		return "restricted"
+	default:
+		return "member"
+	}
+}
+
+func botAPIMemberRestricted(b domain.ChannelBannedRights) bool {
+	return b.SendMessages || b.SendMedia || b.SendStickers || b.SendGifs || b.SendGames ||
+		b.SendInline || b.EmbedLinks || b.SendPolls || b.ChangeInfo || b.InviteUsers ||
+		b.PinMessages || b.ManageTopics || b.SendPhotos || b.SendVideos || b.SendRoundvideos ||
+		b.SendAudios || b.SendVoices || b.SendDocs || b.SendPlain || b.SendReactions
+}
+
 func apiChat(peer domain.Peer, users map[int64]domain.User) map[string]any {
 	switch peer.Type {
 	case domain.PeerTypeUser: