fix(addon): restore Supervisor app management #5732

Job	Run time
Ruff Lint	26s
AST Lint	15s
Docs Size Check	5s
Check uv.lock	13s
Mypy Type Check	35s
Site (astro check + eslint a11y)	38s
Detect relevant changes	5s
Component Version Gate	6s
Unit Tests	1m 48s
Docker & Add-on Validation	1m 12s
E2E Validation (embedded, ubuntu-latest)	1m 49s
E2E Validation (update path)	1m 51s
E2E Validation (ubuntu-latest)	1m 56s
E2E Validation (embedded, ubuntu-24.04-arm)	1m 31s
E2E Validation (ubuntu-24.04-arm)	1m 41s
E2E Validation Gate	3s
	14m 14s

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