Client side signing + smart contract verification is tricky to get right and difficult to debug. Here's a working example with ethers v6 and OpenZeppelin to save you some time.

sign-message.ts

import { ethers, getBytes } from 'ethers';

export async function signMessage(wallet: ethers.Wallet, msg: string) {
  const messageHash = ethers.solidityPackedKeccak256(["string"], [msg])
  const messageHashBytes = getBytes(messageHash)
  const flatSig = await wallet.signMessage(messageHashBytes);
  const sig = ethers.Signature.from(flatSig);
  return {
    v: sig.v,
    r: sig.r,
    s: sig.s,
  }
}

// Example usage
const seed = ethers.sha256(ethers.toUtf8Bytes("this is my private key :)"))
const dummyWallet = new ethers.Wallet(seed)

const message = "Hello World!"
const sig = await signMessage(dummyWallet, message)

// dummyWallet.address "0x83C5fCE9Fc6bf33F8eE0Bfa9F1e7D7359500EbFf"
// sig.v 28
// sig.r "0x2e6d7805bb039c743dedf0b3bdd508d1a5a9520d5f6354116f7f3ca489950946"
// sig.s "0x387de5ed5a65e025e652d21d1a62582a986c8ec6e500f5ec590e6d7d8430c6ca"

verify-message.sol

import {MessageHashUtils} from "@openzeppelin/contracts/utils/cryptography/MessageHashUtils.sol";

address expectedSigner = 0x83C5fCE9Fc6bf33F8eE0Bfa9F1e7D7359500EbFf; // dummyWallet address from sign-message.ts

function verify(string memory message, uint8 v, bytes32 r, bytes32 s) public view returns (bool) {
    bytes32 messageHash = keccak256(abi.encodePacked(message));
    bytes32 ethSignedMessageHash = MessageHashUtils.toEthSignedMessageHash(messageHash);
    address signer = ecrecover(ethSignedMessageHash, v, r, s);
    return signer == expectedSigner;
}

// Example usage
verify(
 "Hello World!",
 28,
 0x2e6d7805bb039c743dedf0b3bdd508d1a5a9520d5f6354116f7f3ca489950946,
 0x387de5ed5a65e025e652d21d1a62582a986c8ec6e500f5ec590e6d7d8430c6ca
);