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.
std::set<int64_t>& setKeyPool = use_split_keypool ? (fReturningInternal ? setInternalKeyPool : setExternalKeyPool) : set_pre_split_keypool;
        
        if (setKeyPool.empty()) {
            return false;
        }
        WalletBatch batch(*database);
        auto it = setKeyPool.begin();
        nIndex = *it;
        setKeyPool.erase(it);
        if (!batch.ReadPool(nIndex, keypool)) {
            throw std::runtime_error(std::string(__func__) + ": read failed");
        }
        CPubKey pk;
        if (!GetPubKey(keypool.vchPubKey.GetID(), pk)) {
            throw std::runtime_error(std::string(__func__) + ": unknown key in key pool");
        }
        
        if (use_split_keypool && keypool.fInternal != fReturningInternal) {
            throw std::runtime_error(std::string(__func__) + ": keypool entry misclassified");
        }
        if (!keypool.vchPubKey.IsValid()) {
            throw std::runtime_error(std::string(__func__) + ": keypool entry invalid");
        }
        m_pool_key_to_index.erase(keypool.vchPubKey.GetID());
        WalletLogPrintf("keypool reserve %d\n", nIndex);
    }
    NotifyCanGetAddressesChanged();
    return true;
}
void CWallet::KeepKey(int64_t nIndex)