What is the type of the parent and child 'provider' for POSClient, to be injected from web3modal

[kombos]

I'm using web3modal (of walletconnect) which provides multiple wallets (metamask, coinbase, qr based mobile wallet connection and others) in my app. web3modal (version 2) internally uses wagmi hooks of ethereum. I'm unable to find the right type of provider for parent and child providers of the configuration to be injected during the init() function of POSClient:

{
    network: ethConfig[selectedEthNetwork]?.network, // 'testnet' or 'mainnet'
    version: ethConfig[selectedEthNetwork]?.version, // 'mumbai' or 'v1'
    parent: {
      provider: parentProvider,
      defaultConfig: {
        from: address,
        chainId: mainnet?.id,
        chain: mainnet?.name,
      },
    },
    child: {
      provider: childProvider,
      defaultConfig: {
        from: address,
        chainId: polygon?.id,
        chain: polygon?.name,
      },
    },
  }

what is the right type of provider to be injected and how to get one from web3modal ? web3modal internally uses ethers.js, but the only example i've seen requires privateKey to create a wallet. what if the privateKey is not accessible (like in case of providers of web3modal v2).