Replaced health checker with Prometheus metrics service.

uv.lock

@@ -924,6 +924,9 @@ wheels = [
 [[package]]
 name = "owncastsentry"
 source = { editable = "." }
+dependencies = [
+    { name = "prometheus-client" },
+]
 
 [package.dev-dependencies]
 dev = [
@@ -941,6 +944,7 @@ dev = [
 ]
 
 [package.metadata]
+requires-dist = [{ name = "prometheus-client", specifier = ">=0.24.1" }]
 
 [package.metadata.requires-dev]
 dev = [
@@ -1069,6 +1073,15 @@ wheels = [
     { url = "https://files.pythonhosted.org/packages/54/20/4d324d65cc6d9205fabedc306948156824eb9f0ee1633355a8f7ec5c66bf/pluggy-1.6.0-py3-none-any.whl", hash = "sha256:e920276dd6813095e9377c0bc5566d94c932c33b27a3e3945d8389c374dd4746", size = 20538, upload-time = "2025-05-15T12:30:06.134Z" },
 ]
 
+[[package]]
+name = "prometheus-client"
+version = "0.24.1"
+source = { registry = "https://pypi.org/simple" }
+sdist = { url = "https://files.pythonhosted.org/packages/f0/58/a794d23feb6b00fc0c72787d7e87d872a6730dd9ed7c7b3e954637d8f280/prometheus_client-0.24.1.tar.gz", hash = "sha256:7e0ced7fbbd40f7b84962d5d2ab6f17ef88a72504dcf7c0b40737b43b2a461f9", size = 85616, upload-time = "2026-01-14T15:26:26.965Z" }
+wheels = [
+    { url = "https://files.pythonhosted.org/packages/74/c3/24a2f845e3917201628ecaba4f18bab4d18a337834c1df2a159ee9d22a42/prometheus_client-0.24.1-py3-none-any.whl", hash = "sha256:150db128af71a5c2482b36e588fc8a6b95e498750da4b17065947c16070f4055", size = 64057, upload-time = "2026-01-14T15:26:24.42Z" },
+]
+
 [[package]]
 name = "prompt-toolkit"
 version = "3.0.52"