Avatar becomes invisible when changing wearables

### Build version
v0.176.0-alpha-main

### Issue Description
Changing wearables causes the player's avatar to become fully invisible. The reporter suspects the issue may be triggered specifically when purchasing a new wearable and then equipping it, but it is not confirmed. The issue is not location-specific — it occurs everywhere in the explorer (not just in arena scenes).

### STR (Steps to Reproduce)
1. Launch the Explorer and log in
2. Navigate to the backpack/wearables section
3. Change an equipped wearable (possibly: purchase a new wearable first, then equip it)
4. Observe the avatar in-world

### Expected Result
Avatar remains visible after changing wearables.

### Actual Result with evidence
Avatar becomes invisible after the wearable change. Confirmed on Windows 11 with an NVIDIA GeForce RTX 5080 Laptop GPU (Direct3D 11.0, VRAM: 16003 MB, Driver: 32.0.15.9191). No relevant errors were found in the attached log (wearable/avatar error logging is disabled in production).

**Hardware:** ROG Strix SCAR 18 G835LW — Intel Core Ultra 9 275HX, 32 GB RAM, RTX 5080 Laptop GPU
**Unity Version:** 6000.5.9f1

### Reproduction
Always (100% reported by user)

### Operative system and additional Notes
Windows 11 (10.0.26200)

Additional context from reporter: The arena scene where the issue was recorded is irrelevant — the bug occurs across all locations.

**Related issues:**
- #9110 — Avatars disappear after in-session account switch (similar disappearance symptom, different trigger)

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Reported by Matt
Requested by Dawid Krajewski (<@U079GRD9WTZ>)

Start by reproducing the issue in the Unity Explorer: log in, open the backpack/wearables section, change an equipped wearable, and observe the avatar in-world. Check the wearable and avatar visibility flow around the reported purchase-then-equip scenario, using issue #9110 only as related context. Done means the avatar remains visible after changing wearables across Explorer locations.

Written by the indexing model from the issue text.