rules.http.paths.path で正規表現でマッチさせたものが
metadata.annotations.nginx.ingress.kubernetes.io/rewrite-target に入ります。
apiVersion: networking.k8s.io/v1
kind: Ingress
metadata:
  name: my-ingress
  namespace: my-namespace
  annotations:
    ingress.kubernetes.io/ssl-redirect: "true"
    nginx.ingress.kubernetes.io/rewrite-target: /api/apppath/$1
spec:
  tls:
    - secretName: my-http-cert
  rules:
    - host: log.ytyng.com
      http:
        paths:
          - path: /(.*)
            pathType: Prefix
            backend:
              service:
                name: my-service-service
                port:
                  number: 8000