Contemporary extended reality (XR) systems deliver high-fidelity visual and spatial-audio immersion, yet the cognitive and affective states of the user remain invisible to the virtual environment. We present PiEEG XR, an open-source platform that bridges consumer-grade electroencephalography (EEG) hardware with WebXR-based mixed reality to produce real-time, neural-adaptive avatar behaviour. The system acquires multi-channel EMG at 250 Hz with 24-bit resolution via Bluetooth Low Energy 5 (BLE5), derives five canonical frequency-band power features (delta, theta, alpha, beta, gamma) using a rolling-window Fast Fourier Transform, and maps the resulting affective state estimates to VRM avatar facial expressions and interaction affordances rendered through a React Three Fiber / Three.js pipeline on the Meta Quest browser. A lightweight OSC bridge enables simultaneous streaming to social VR platforms such as VRChat. We describe the system design, the EEG-to-expression mapping heuristic, the WebXR spatial anchoring strategy, and an OSC parameter protocol. PiEEG XR represents an accessible entry point for affective computing research in immersive environments and demonstrates that production-ready neural-adaptive avatars can be deployed entirely within an open browser stack.