[QA] Games | Bowling scoring text desync and asymmetric join (Fastlane Bowling)

### 🛠️ **Build version:**
N/A

### 📔 **Issue Description:**

Two related bugs reported at Fastlane Bowling on Mac:

**1. Scoring text / graphics desync**
The on-screen result text shows "gutter ball" even when the score correctly registers the knocked-down pins (e.g. "2 pins") and the pin-fall animation visually plays. The UI label and the simulation/score state are out of sync.

**2. Asymmetric game join**
A player cannot join a lane when another user has started the game (pre-game lobby). However, the reverse works: other players *can* join a game started by the same user. This suggests the join flow behaves differently depending on who is the host.

### 👣 **STR:**

1. Go to Fastlane Bowling with at least one other user.
2. Have the other user start a game — attempt to join their lane before it starts → **unable to join**.
3. Start a game yourself — have the other user attempt to join your lane → **join succeeds**.
4. During a game, bowl and observe the result text vs. the score counter and pin-fall animation.
- Note whether the text label matches the actual pins knocked down.

### ✔️ **Expected Result:**
- Players can join any lane before a game starts, regardless of who initiated it.
- The result text (e.g. "gutter ball", "2 pins") always matches the score and the pin-fall animation.

### ❌ **Actual Result:**
- Joining another user's lane before the game starts fails.
- Result text shows "gutter ball" while the score and animation correctly reflect pins knocked down.

### ➗ **Reproduction:**
⚠️ Intermittent (~50%)

### 🖥️ **Operative system:**
Mac

### 🔗 **Related issues:**
- #9375 — Unable to move in Fastlane Bowling (multi-user spawn issue)

### 📎 **Additional context:**
Reported via bug-report channel on 2026-08-24. Reporter observed the desync personally and confirmed the asymmetric join with a second user (Eve). Screenshots attached in Slack thread.

No source file, test, or entry point is named. Start by reproducing both Fastlane Bowling failures with two users on Mac, then trace the lane-join flow and scoring/result display; done means any player can join a pre-game lane and the result text matches the score and pin-fall animation reliably.

Written by the indexing model from the issue text.