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.
} else if (PeerHasHeader(&state, pindex)) {
                        continue; 
                    } else if (pindex->pprev == nullptr || PeerHasHeader(&state, pindex->pprev)) {
                        
                        
                        fFoundStartingHeader = true;
                        vHeaders.push_back(pindex->GetBlockHeader());
                    } else {
                        
                        
                        fRevertToInv = true;
                        break;
                    }
                }
            }
            if (!fRevertToInv && !vHeaders.empty()) {
                if (vHeaders.size() == 1 && state.fPreferHeaderAndIDs) {
                    
                    
                    LogPrint(BCLog::NET, "%s sending header-and-ids %s to peer=%d\n", __func__,
                            vHeaders.front().GetHash().ToString(), pto->GetId());
                    int nSendFlags = state.fWantsCmpctWitness ? 0 : SERIALIZE_TRANSACTION_NO_WITNESS;
                    bool fGotBlockFromCache = false;
                    {
                        LOCK(cs_most_recent_block);
                        if (most_recent_block_hash == pBestIndex->GetBlockHash()) {
                            if (state.fWantsCmpctWitness || !fWitnessesPresentInMostRecentCompactBlock)
                                connman->PushMessage(pto, msgMaker.Make(nSendFlags, NetMsgType::CMPCTBLOCK, *most_recent_compact_block));
                            else {
                                CBlockHeaderAndShortTxIDs cmpctblock(*most_recent_block, state.fWantsCmpctWitness);