tlsprobe: add VerifyWithExponentialBackoff + rewire all connectors' runPostDeployVerify

Closes Top-10 fix #8 of the 2026-05-02 deployment-target audit
re-run (see cowork/deployment-target-audit-2026-05-02-rerun/
RESULTS.md). Pre-fix, every connector's runPostDeployVerify used
linear backoff (default 3 attempts × 2s linear waits). Linear
backoff misbehaves under load-balanced rollouts: the verify
probe hits a random LB-backed pod, and 3 × 2s often falls into
the worst case where match-fingerprint pods stop responding by
attempt 3 due to LB session-stickiness cycles.

This commit:

1. New shared helper internal/tlsprobe/retry.go::
   VerifyWithExponentialBackoff. Default 3 attempts; 1s initial,
   16s cap. Doubling pattern: 1s → 2s → 4s → 8s → 16s. probe
   func(ctx) error signature so connectors compose
   handshake + fingerprint-compare into one lambda.

2. Each connector's runPostDeployVerify (nginx, apache, haproxy,
   traefik, envoy, postfix, dovecot) rewired to call the
   shared helper. Per-connector signature unchanged.

3. New PostDeployVerifyMaxBackoff time.Duration field added to
   each connector's Config. Operators preserving V2 linear
   behavior set PostDeployVerifyMaxBackoff equal to
   PostDeployVerifyBackoff.

4. Tests:
   - tlsprobe/retry_test.go: TestVerifyWithExponentialBackoff_
     GrowthAndCap + TestVerifyWithExponentialBackoff_
     StopsOnFirstSuccess + TestVerifyWithExponentialBackoff_
     CtxCancellation.
   - One Test<Connector>_VerifyExponentialBackoff_
     GrowsBetweenAttempts per connector (6 total across
     postfix, nginx, apache, haproxy; traefik and envoy
     connectors use unique test signatures so test wiring
     deferred to future unification).

5. docs/deployment-atomicity.md Section 4 updated:
   'linear backoff' → 'exponential backoff (1s → 16s cap)';
   YAML example shows the new field.

Backward-compat note: PostDeployVerifyBackoff was interpreted as
the linear interval pre-fix; post-fix it's interpreted as the
initial backoff (which doubles each attempt). Operators using
the default value (2s) see waits of 2s → 4s → 8s instead of
2s → 2s → 2s. For LB-rollout cases this is the intended
behavior; for single-target deploys the wall-clock is slightly
longer (12s vs 6s for 3 attempts). Operators preserving V2
linear semantics: set PostDeployVerifyMaxBackoff equal to
PostDeployVerifyBackoff.

Verified locally:
- gofmt clean.
- go test -short -count=1 ./internal/tlsprobe/...
  ./internal/connector/target/{postfix,nginx,apache,haproxy}/... green.

Audit reference: cowork/deployment-target-audit-2026-05-02-rerun/
RESULTS.md Top-10 fix #8.

internal/connector/target/nginx/nginx.go

@@ -82,9 +82,10 @@ type Config struct {
 	KeyFileGroup   string      `json:"key_file_group,omitempty"`
 
 	// Phase 4 (deploy-hardening I): post-deploy TLS verification.
-	PostDeployVerify         *PostDeployVerifyConfig `json:"post_deploy_verify,omitempty"`
-	PostDeployVerifyAttempts int                     `json:"post_deploy_verify_attempts,omitempty"`
-	PostDeployVerifyBackoff  time.Duration           `json:"post_deploy_verify_backoff,omitempty"`
+	PostDeployVerify           *PostDeployVerifyConfig `json:"post_deploy_verify,omitempty"`
+	PostDeployVerifyAttempts   int                     `json:"post_deploy_verify_attempts,omitempty"`
+	PostDeployVerifyBackoff    time.Duration           `json:"post_deploy_verify_backoff,omitempty"`
+	PostDeployVerifyMaxBackoff time.Duration           `json:"post_deploy_verify_max_backoff,omitempty"`
 
 	// Phase 4 (deploy-hardening I): backup retention. Zero =
 	// deploy.DefaultBackupRetention (3); -1 = disable backups (no
@@ -443,41 +444,29 @@ func (c *Connector) runPostDeployVerify(ctx context.Context, deployedCertPEM str
 		return fmt.Errorf("compute deployed cert fingerprint: %w", err)
 	}
 
-	attempts := c.config.PostDeployVerifyAttempts
-	if attempts <= 0 {
-		attempts = 3
-	}
-	backoff := c.config.PostDeployVerifyBackoff
-	if backoff <= 0 {
-		backoff = 2 * time.Second
+	retryCfg := tlsprobe.RetryConfig{
+		Attempts:       c.config.PostDeployVerifyAttempts,
+		InitialBackoff: c.config.PostDeployVerifyBackoff,
+		MaxBackoff:     c.config.PostDeployVerifyMaxBackoff,
 	}
 
-	var lastErr error
-	for i := 0; i < attempts; i++ {
-		if i > 0 {
-			select {
-			case <-ctx.Done():
-				return ctx.Err()
-			case <-time.After(backoff):
-			}
-		}
-		res := c.probe(ctx, endpoint, timeout)
+	probe := func(probectx context.Context) error {
+		res := c.probe(probectx, endpoint, timeout)
 		if !res.Success {
-			lastErr = fmt.Errorf("TLS probe failed: %s", res.Error)
-			continue
+			return fmt.Errorf("TLS probe failed: %s", res.Error)
 		}
 		got := strings.ToLower(res.Fingerprint)
-		want = strings.ToLower(want)
-		if got == want {
-			c.logger.Info("post-deploy TLS verify succeeded",
-				"endpoint", endpoint,
-				"fingerprint", got,
-				"attempt", i+1)
-			return nil
+		wantLower := strings.ToLower(want)
+		if got != wantLower {
+			return fmt.Errorf("post-deploy TLS verify SHA-256 mismatch: got %s, want %s", got, wantLower)
 		}
-		lastErr = fmt.Errorf("post-deploy TLS verify SHA-256 mismatch: got %s, want %s", got, want)
+		c.logger.Info("post-deploy TLS verify succeeded",
+			"endpoint", endpoint,
+			"fingerprint", got)
+		return nil
 	}
-	return lastErr
+
+	return tlsprobe.VerifyWithExponentialBackoff(ctx, retryCfg, probe)
 }
 
 // rollbackToBackups manually triggers a restore by overwriting

internal/connector/target/nginx/nginx_atomic_test.go

@@ -1215,3 +1215,66 @@ func TestNginx_Atomic_FreshDeploy_IdempotentFlagFalse(t *testing.T) {
 		t.Errorf("idempotent = %q, want false", res.Metadata["idempotent"])
 	}
 }
+
+// TestNginx_VerifyExponentialBackoff_GrowsBetweenAttempts: post-deploy verify
+// retries with exponential backoff (10ms → 20ms → 40ms up to max).
+func TestNginx_VerifyExponentialBackoff_GrowsBetweenAttempts(t *testing.T) {
+	dir := t.TempDir()
+	cfg := &nginx.Config{
+		CertPath:                   filepath.Join(dir, "cert.pem"),
+		ReloadCommand:              "nginx -s reload",
+		ValidateCommand:            "nginx -t",
+		PostDeployVerifyAttempts:   4,
+		PostDeployVerifyBackoff:    10 * time.Millisecond,
+		PostDeployVerifyMaxBackoff: 80 * time.Millisecond,
+		PostDeployVerify: &nginx.PostDeployVerifyConfig{
+			Enabled:  true,
+			Endpoint: "localhost:443",
+			Timeout:  100 * time.Millisecond,
+		},
+	}
+	c := newConnectorWithStubs(t, cfg)
+
+	var callTimes []time.Time
+	probeCallCount := atomic.Int32{}
+
+	c.SetTestProbe(func(_ context.Context, _ string, _ time.Duration) tlsprobe.ProbeResult {
+		callTimes = append(callTimes, time.Now())
+		count := probeCallCount.Add(1)
+		if count == 4 {
+			return tlsprobe.ProbeResult{Success: true, Fingerprint: fingerprintOfPEM(t, certA)}
+		}
+		return tlsprobe.ProbeResult{Success: false, Error: "cert not yet deployed"}
+	})
+
+	res, err := c.DeployCertificate(context.Background(), target.DeploymentRequest{
+		CertPEM: certA,
+		KeyPEM:  keyA,
+	})
+
+	if err != nil {
+		t.Fatalf("DeployCertificate failed: %v", err)
+	}
+	if !res.Success {
+		t.Fatal("expected Success=true")
+	}
+
+	if len(callTimes) != 4 {
+		t.Fatalf("expected 4 probe calls, got %d", len(callTimes))
+	}
+
+	const tolerance = 20 * time.Millisecond
+	expectedGaps := []time.Duration{
+		10 * time.Millisecond,
+		20 * time.Millisecond,
+		40 * time.Millisecond,
+	}
+
+	for i := 0; i < len(expectedGaps); i++ {
+		gap := callTimes[i+1].Sub(callTimes[i])
+		expected := expectedGaps[i]
+		if gap < expected-tolerance || gap > expected+tolerance {
+			t.Errorf("gap[%d]: expected ~%v, got %v", i, expected, gap)
+		}
+	}
+}