fix(addon): restore Supervisor app management #5756

Job	Run time
Docs Size Check	13s
Ruff Lint	31s
AST Lint	18s
Detect relevant changes	10s
Mypy Type Check	33s
Component Version Gate	9s
Site (astro check + eslint a11y)	45s
Docker & Add-on Validation	1m 8s
Check uv.lock	12s
Unit Tests	4m 19s
E2E Validation (ubuntu-latest)	5m 44s
E2E Validation (embedded, ubuntu-24.04-arm)	5m 5s
E2E Validation (embedded, ubuntu-latest)	6m 23s
E2E Validation (update path)	3m 26s
E2E Validation (ubuntu-24.04-arm)	4m 38s
E2E Validation Gate	2s
	33m 36s

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