The `Broadcast`/`ResendWalletTransactions` interface is strange:

- it's the node saying to the wallet "Try to submit your unconfirmed transactions to the mempool again"
- it's called in one place by the node, in `SendMessages()` here: https://github.com/bitcoin/bitcoin/blob/c033c4b5cef89a654e4d9d5c5f9bd823871b068b/src/net_processing.cpp#L3515. `SendMessages()` is called on the message handling thread on a loop.
- the actual scheduling of when the wallet sends messages is handled in the `ResendWalletTransactions()` function itself, using the `nNextResend` and `nLastResend` wallet globals (which could as easily be static variables in `ResendWalletTransactions()`).

Therefore the only use of `Broadcast()` is to periodically prod the wallet. The wallet itself decides whether it's time to resend transactions. This could be done by scheduling regular calls to `ResendWalletTransactions()`, in the same way that we schedule regular wallet flushes here: https://github.com/bitcoin/bitcoin/blob/c033c4b5cef89a654e4d9d5c5f9bd823871b068b/src/wallet/init.cpp#L215.

A couple of minor implementation details:

- the call to `Broadcast()` in `SendMessages()` is protected by an if statement `if (!fReindex && !fImporting && !IsInitialBlockDownload()) {`. Those tests could be moved into `ResendWalletTransactions()` (through the `Chain` interface).
- The `Broadcast` notification passes in the `nTimeBestReceived` time of the best block. That could be fetched by `ResendWalletTransactions()` through the `Chain` interface.
return batch.WriteKey(pubkey,
                                                 secret.GetPrivKey(),
                                                 mapKeyMetadata[pubkey.GetID()]);
    }
    UnsetWalletFlag(WALLET_FLAG_BLANK_WALLET);
    return true;
}
bool CWallet::AddKeyPubKey(const CKey& secret, const CPubKey &pubkey)
{
    WalletBatch batch(*database);
    return CWallet::AddKeyPubKeyWithDB(batch, secret, pubkey);
}
bool CWallet::AddCryptedKey(const CPubKey &vchPubKey,
                            const std::vector<unsigned char> &vchCryptedSecret)
{
    if (!CCryptoKeyStore::AddCryptedKey(vchPubKey, vchCryptedSecret))
        return false;
    {
        LOCK(cs_wallet);
        if (encrypted_batch)
            return encrypted_batch->WriteCryptedKey(vchPubKey,
                                                        vchCryptedSecret,
                                                        mapKeyMetadata[vchPubKey.GetID()]);
        else
            return WalletBatch(*database).WriteCryptedKey(vchPubKey,
                                                            vchCryptedSecret,
                                                            mapKeyMetadata[vchPubKey.GetID()]);
    }
}
void CWallet::LoadKeyMetadata(const CKeyID& keyID, const CKeyMetadata& meta)