Add verified Truthtrance hand inventory questions

Players can ask total-hand and primary-role card-count comparisons using the
existing count controls and compound facts. Component presentation shares the
same default-role classification, including canonical Richese cards, Ix alternate
uses, and Ecaz slot-only specials. Only the respondent receives the verified
aggregate answer; current facts do not impose future custody promises.

Eight new tests cover all 60 catalog cards, real engine actions, malformed input,
private worlds, all four bots, JSON continuation, and a legal custody transfer.
Expanded production-room SQLite cases cover restored total/category/compound
facts, suspended auction state, and one winning concurrent answer/discard.
Independent review's two copy issues were fixed before broad verification.

Validation: types, lint and 4,200 offline tests passed; production build passed;
40 HTTP tests passed. One stable broad run (check 123036 ms, build 6505 ms,
integration 23467 ms). Browser room LC3E55GY verified combined role counts,
total hand size, invalid-input feedback and refresh at 390px phone width.
All 33 pre-integration rooms preserved unchanged; HTTP checks added 30 rooms.
No complete-mode, full-game or publication gate opened.

Private report: 20260913-hand-inventory-final/report.json
Source fingerprint: c6a69a9e69941cdd1e5734d92afedbf10d31fda36c91d26ca7e15f4fb7c59b18
Efficiency pilot milestone 3: aggregate counter 58,695,053 to 59,144,653 at
completed verification = 449,600 tokens, including context/coordination overhead.
Two bounded workhorse-model helpers, reused UI and SQLite fixtures, one browser
room. Counter is not monetary cost and this differently sized batch does not
establish a savings percentage. Final Git/push overhead follows this sample.

game/card-presentation.ts

@@ -3,6 +3,7 @@ import { BATTLE_CARD_HELP, battleCardLabel } from './battle-cards';
 import { RULE_TOPICS, type RuleTopic } from './reference';
 import { ecazTreacheryDefinition } from './ecaz-cards';
 import { richeseCardDefinition } from './richese-cards';
+import { printedCardCategory } from './card-category';
 
 /** Presentation uses only a card the caller has already been authorized to see. */
 export type VisibleCard = Readonly<
@@ -130,15 +131,13 @@ export function cardPresentation(card: VisibleCard): CardPresentation {
   const topics = topicIds
     .map((id) => RULE_TOPICS.find((topic) => topic.id === id))
     .filter((topic): topic is RuleTopic => !!topic);
-  const role = ['shield', 'snooper', 'shieldSnooper', 'chemistry'].includes(
-    card.kind,
-  )
-    ? 'defense'
-    : card.kind === 'hero'
+  const category = printedCardCategory(card);
+  const role =
+    category === 'hero'
       ? 'leader'
-      : card.kind === 'special' || card.kind === 'worthless'
+      : category === 'special' || category === 'worthless'
         ? 'utility'
-        : 'weapon';
+        : category;
   return {
     category:
       card.kind === 'special'