feat(stats): best-move word, moves & hint-share, and a hint-count fix (#81)

The statistics screen gains real depth, plus a hint-count bug fix found along the way.

- Best move per variant: the screen shows the actual best-move word (drawn as game
  tiles; a wildcard shows its letter but no value), broken down by game variant, empty
  variants omitted. New account_best_move table, written at game finish.
- Moves & hint share: two new lifetime tiles — the player's play count and the share of
  plays that used a hint — from summed account_stats counters (moves, hints_used).
  Honest-AI games are excluded, like the rest of the stats.
- Hint-count fix: the in-game hint badge no longer goes stale across games. The global
  wallet now rides the wire apart from the per-game allowance (wallet_balance on
  StateView/HintResult/StatsView), so the client reads the live wallet rather than a
  per-game snapshot; game_players.hints_used now counts every hint (allowance + wallet),
  its true per-game total.
- Account merge: sums the new moves/hints_used counters and merges the per-variant best
  moves (higher score kept), which it previously dropped.
- Admin: the user card shows Moves and Hints used.
- UI polish: tab/label wording, game-over text, and e2e selectors hardened against label
  changes.

All wire additions are trailing (backward-compatible). Docs (ARCHITECTURE, FUNCTIONAL +ru,
UISN_DESIGN) updated in step.

gateway/internal/backendclient/api.go

@@ -162,6 +162,7 @@ type StateResp struct {
 	Rack           []int               `json:"rack"`
 	BagLen         int                 `json:"bag_len"`
 	HintsRemaining int                 `json:"hints_remaining"`
+	WalletBalance  int                 `json:"wallet_balance"`
 	Alphabet       []AlphabetEntryJSON `json:"alphabet,omitempty"`
 }
 
@@ -331,6 +332,7 @@ func (c *Client) ChatPost(ctx context.Context, userID, gameID, body, clientIP st
 type HintResultResp struct {
 	Move           MoveRecordResp `json:"move"`
 	HintsRemaining int            `json:"hints_remaining"`
+	WalletBalance  int            `json:"wallet_balance"`
 }
 
 // EvalResultResp is an unlimited move preview. Dir is the orientation the backend

gateway/internal/backendclient/api_social.go

@@ -47,13 +47,33 @@ type BlockListResp struct {
 	Blocked []AccountRefResp `json:"blocked"`
 }
 
-// StatsResp is a durable account's lifetime statistics.
+// StatsResp is a durable account's lifetime statistics. BestMoves breaks the best move
+// down per variant, carrying the word itself; it is absent for an account with no recorded
+// play and lists only variants the account has played.
 type StatsResp struct {
-	Wins          int `json:"wins"`
-	Losses        int `json:"losses"`
-	Draws         int `json:"draws"`
-	MaxGamePoints int `json:"max_game_points"`
-	MaxWordPoints int `json:"max_word_points"`
+	Wins          int            `json:"wins"`
+	Losses        int            `json:"losses"`
+	Draws         int            `json:"draws"`
+	MaxGamePoints int            `json:"max_game_points"`
+	MaxWordPoints int            `json:"max_word_points"`
+	Moves         int            `json:"moves"`
+	HintsUsed     int            `json:"hints_used"`
+	BestMoves     []BestMoveResp `json:"best_moves"`
+}
+
+// BestMoveResp is one variant's best play: the variant label, the play's total score and
+// its main word as ordered tiles (letter, value, blank — value 0 for a blank).
+type BestMoveResp struct {
+	Variant string             `json:"variant"`
+	Score   int                `json:"score"`
+	Word    []BestMoveTileResp `json:"word"`
+}
+
+// BestMoveTileResp is one letter cell of a best-move word.
+type BestMoveTileResp struct {
+	Letter string `json:"letter"`
+	Value  int    `json:"value"`
+	Blank  bool   `json:"blank"`
 }
 
 // InvitationInviteeResp is one invitee's seat and response with their name.