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.
if (nChangePosInOut == -1 && nSubtractFeeFromAmount == 0 && pick_new_inputs) {
                        unsigned int tx_size_with_change = nBytes + coin_selection_params.change_output_size + 2; 
                        CAmount fee_needed_with_change = GetMinimumFee(*this, tx_size_with_change, coin_control, nullptr);
                        CAmount minimum_value_for_change = GetDustThreshold(change_prototype_txout, discard_rate);
                        if (nFeeRet >= fee_needed_with_change + minimum_value_for_change) {
                            pick_new_inputs = false;
                            nFeeRet = fee_needed_with_change;
                            continue;
                        }
                    }
                    
                    if (nFeeRet > nFeeNeeded && nChangePosInOut != -1 && nSubtractFeeFromAmount == 0) {
                        CAmount extraFeePaid = nFeeRet - nFeeNeeded;
                        std::vector<CTxOut>::iterator change_position = txNew.vout.begin()+nChangePosInOut;
                        change_position->nValue += extraFeePaid;
                        nFeeRet -= extraFeePaid;
                    }
                    break; 
                }
                else if (!pick_new_inputs) {