React Redux filtered by array onChange input

help me please in Redux filter onInput change! I have two state: 1) items - is array (name number and tel number), 2) search (this state get value by input). When i enter name and phone number and click onSubmit in component will sent state "items". The next i see this contacts on the page. I have another input, his task, filter by contacts array. How can i filtered array state no change him and when filter value === '' i can see all items in state "items".

myStore

import { configureStore } from "@reduxjs/toolkit";
import { createSlice } from "@reduxjs/toolkit";

const contactsSlice = createSlice({
  name: "contacts",
  initialState: {
    items: [],
    search: "",
  },
  reducers: {
    add(state, action) {
      state.items.push(action.payload);
    },
    remove(state, action) {
      state.items = state.items.filter((arrow) => arrow.id !== action.payload);
    },
    search(state, action) {
      state.search = action.payload;

      state.items.filter((item) =>
        item.name.toLowerCase().includes(state.search)
      );
    },
  },
});

export const { add, remove, search } = contactsSlice.actions;

export const store = configureStore({
  reducer: {
    contacts: contactsSlice.reducer,
  },
});

My Component Filter

import { useSelector, useDispatch } from "react-redux";
import { ContainerSearch, Title, Input } from "./Filter.styled";
import { search } from "../Redux/store";

const Filter = () => {
  const dispatch = useDispatch();

  const onChange = (e) => {
    dispatch(search(e.currentTarget.value.toLocaleLowerCase()));
  };

  return (
    <ContainerSearch>
      <Title>Find contacts by name</Title>
      <Input type="text" onChange={onChange} placeholder="Search name" />
    </ContainerSearch>
  );
};

export default Filter;

and my List items

import { useSelector, useDispatch } from "react-redux";
import { remove } from "../Redux/store";
import {
  ContainerList,
  Title,
  Wrapper,
  Item,
  ButtonClose,
  TextList,
} from "./ContactList.styled";

export const List = () => {
  const selector = useSelector((state) => state.contacts.items);
  const dispatch = useDispatch();

  const deleteContact = (contactId) => {
    dispatch(remove(contactId));
  };

  return (
    <ContainerList>
      <Title>Contacts</Title>
      {selector.length > 0 ? (
        <Wrapper>
          {selector.map(({ id, name, number }, index) => (
            <Item key={id} index={index}>
              {name} : {number}
              <ButtonClose onClick={() => deleteContact(id)}>
                &#10007;
              </ButtonClose>
            </Item>
          ))}
        </Wrapper>
      ) : (
        <TextList>No Contacts</TextList>
      )}
    </ContainerList>
  );
};