Add the provider Checker contract and the kubernetes and GCP checks

Checker is an optional interface next to Provider: Check returns one
verdict per target and never fails as a whole. The kubernetes provider
lists at most one managed Pod cluster-wide (the verb and scope GC relies
on); the GCP provider fetches a single page of at most one managed
instance through a new Probe seam method, since the SDK treats
MaxResults as a page size and the existing AggregatedList drains every
page.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

docs/plans-executions/2026-09-11-1526-provider-health-checks.md

@@ -3,7 +3,7 @@ Plan: [docs/plans/2026-09-11-1526-provider-health-checks.md](../plans/2026-09-11
 
 - [x] Step 0 — Save the plan
 - [x] Step 1 — ProviderHealth API and CRD
-- [ ] Step 2 — Contract plus the kubernetes and GCP checks
+- [x] Step 2 — Contract plus the kubernetes and GCP checks
 - [ ] Step 3 — KVM check
 - [ ] Step 4 — Monitor
 - [ ] Step 5 — Metrics and wiring
@@ -58,3 +58,40 @@ Worth noting:
   round-trip in Step 4.
 - `config/rbac/role.yaml` is unchanged so far. The manager's own permissions arrive in
   Step 4 with the Monitor's RBAC markers.
+
+## Step 2 — Contract plus the kubernetes and GCP checks
+
+`provider.Checker` is an optional interface in `internal/provider/check.go`, kept out of
+`Provider`. Each implementation has a compile-time assertion, because the monitor's
+type assertion would otherwise fail silently.
+
+- **kubernetes:** lists at most one managed Pod cluster-wide, using the same client, verb
+  and scope as `ListByTag`. The target is `apiserver`, at the `restCfg.Host` now stored
+  in the new `apiHost` field.
+- **GCP:** calls a new seam method, `Probe`. `realInstances.Probe` lives in `check.go`,
+  next to its only caller. `ListByTag`'s `Sprintf` filter became the shared
+  `managedFilter` constant, so the check and the GC sweep can't drift apart.
+
+Before relying on "MaxResults is only a page size", I checked the SDK's REST
+`AggregatedList` in the module cache:
+
+```bash
+grep -n "func (c \*instancesRESTClient) AggregatedList" -A80 \
+  "$(go list -m -f '{{.Dir}}' cloud.google.com/go/compute)"/apiv1/instances_client.go
+# InternalFetch: req.MaxResults = pageSize ... return elems, resp.GetNextPageToken(), nil
+```
+
+```bash
+go build ./... && go vet ./internal/provider/... && go test -race -count=1 ./internal/provider/...
+```
+
+Worth noting:
+- The planned `TestRealInstances_Probe_fetchesOnePage` became a three-case
+  `TestRealInstances_Probe` table.
+  - It keeps the first page's `nextPageToken`, and asserts exactly one request with
+    `maxResults=1` for each case.
+  - "empty project" covers `iterator.Done`.
+  - "api error keeps its status" proves the real client returns a `*googleapi.Error`, so
+    a disabled Compute API is reported as `Forbidden` rather than `Unreachable`.
+- Once a context has ended, both checks report `Timeout` whatever the error says. The
+  monitor's timeout is the usual cause, and the underlying error only repeats it.