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 (pto->nVersion >= FEEFILTER_VERSION && gArgs.GetBoolArg("-feefilter", DEFAULT_FEEFILTER) &&
            !(pto->fWhitelisted && gArgs.GetBoolArg("-whitelistforcerelay", DEFAULT_WHITELISTFORCERELAY))) {
            CAmount currentFilter = mempool.GetMinFee(gArgs.GetArg("-maxmempool", DEFAULT_MAX_MEMPOOL_SIZE) * 1000000).GetFeePerK();
            int64_t timeNow = GetTimeMicros();
            if (timeNow > pto->nextSendTimeFeeFilter) {
                static CFeeRate default_feerate(DEFAULT_MIN_RELAY_TX_FEE);
                static FeeFilterRounder filterRounder(default_feerate);
                CAmount filterToSend = filterRounder.round(currentFilter);
                
                filterToSend = std::max(filterToSend, ::minRelayTxFee.GetFeePerK());
                if (filterToSend != pto->lastSentFeeFilter) {
                    connman->PushMessage(pto, msgMaker.Make(NetMsgType::FEEFILTER, filterToSend));
                    pto->lastSentFeeFilter = filterToSend;
                }
                pto->nextSendTimeFeeFilter = PoissonNextSend(timeNow, AVG_FEEFILTER_BROADCAST_INTERVAL);
            }
            
            
            else if (timeNow + MAX_FEEFILTER_CHANGE_DELAY * 1000000 < pto->nextSendTimeFeeFilter &&
                     (currentFilter < 3 * pto->lastSentFeeFilter / 4 || currentFilter > 4 * pto->lastSentFeeFilter / 3)) {
                pto->nextSendTimeFeeFilter = timeNow + GetRandInt(MAX_FEEFILTER_CHANGE_DELAY) * 1000000;
            }
        }
    }
    return true;
}
class CNetProcessingCleanup