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.
for (auto it = group.m_outputs.begin(); it != group.m_outputs.end(); ) {
                const CInputCoin& coin = *it;
                CAmount effective_value = coin.txout.nValue - (coin.m_input_bytes < 0 ? 0 : coin_selection_params.effective_fee.GetFee(coin.m_input_bytes));
                
                if (effective_value > 0) {
                    group.fee += coin.m_input_bytes < 0 ? 0 : coin_selection_params.effective_fee.GetFee(coin.m_input_bytes);
                    group.long_term_fee += coin.m_input_bytes < 0 ? 0 : long_term_feerate.GetFee(coin.m_input_bytes);
                    group.effective_value += effective_value;
                    ++it;
                } else {
                    it = group.Discard(coin);
                }
            }
            if (group.effective_value > 0) utxo_pool.push_back(group);
        }
        
        CAmount not_input_fees = coin_selection_params.effective_fee.GetFee(coin_selection_params.tx_noinputs_size);
        bnb_used = true;
        return SelectCoinsBnB(utxo_pool, nTargetValue, cost_of_change, setCoinsRet, nValueRet, not_input_fees);
    } else {
        
        for (const OutputGroup& group : groups) {
            if (!group.EligibleForSpending(eligibility_filter)) continue;
            utxo_pool.push_back(group);
        }
        bnb_used = false;
        return KnapsackSolver(nTargetValue, utxo_pool, setCoinsRet, nValueRet);
    }
}
bool CWallet::SelectCoins(const std::vector<COutput>& vAvailableCoins, const CAmount& nTargetValue, std::set<CInputCoin>& setCoinsRet, CAmount& nValueRet, const CCoinControl& coin_control, CoinSelectionParams& coin_selection_params, bool& bnb_used) const