fix(desktop): own native WebSocket lifecycle #10340

Job	Run time
Detect Changed Paths	7s
Dead Token Reference Guard	6s
Windows Rust (x86_64-pc-windows-msvc)	8m 2s
Desktop Build (macOS)	5m 11s
Rust Lint	3m 45s
Desktop Core	6m 7s
Desktop E2E Relay	17s
Desktop Smoke E2E (3)	6m 29s
Desktop Smoke E2E (2)	8m 30s
Desktop Smoke E2E (1)	8m 41s
Desktop Smoke E2E (4)	9m 55s
Security	0s
Mobile	0s
Unit Tests	0s
Web	0s
Server Cross-Compile	0s
Desktop E2E Integration (1/2)	4m 44s
Desktop E2E Integration (2/2)	5m 58s
Backend Integration (relay e2e)	0s
Relay E2E	0s
Desktop E2E Integration	2s
Desktop	4s
	1h 7m 58s

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