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 (!txinfo.tx) {
                        continue;
                    }
                    if (filterrate && txinfo.feeRate.GetFeePerK() < filterrate) {
                        continue;
                    }
                    if (pto->pfilter && !pto->pfilter->IsRelevantAndUpdate(*txinfo.tx)) continue;
                    
                    vInv.push_back(CInv(MSG_TX, hash));
                    nRelayedTransactions++;
                    {
                        
                        while (!vRelayExpiration.empty() && vRelayExpiration.front().first < nNow)
                        {
                            mapRelay.erase(vRelayExpiration.front().second);
                            vRelayExpiration.pop_front();
                        }
                        auto ret = mapRelay.insert(std::make_pair(hash, std::move(txinfo.tx)));
                        if (ret.second) {
                            vRelayExpiration.push_back(std::make_pair(nNow + 15 * 60 * 1000000, ret.first));
                        }
                    }
                    if (vInv.size() == MAX_INV_SZ) {
                        connman->PushMessage(pto, msgMaker.Make(NetMsgType::INV, vInv));
                        vInv.clear();
                    }
                    pto->filterInventoryKnown.insert(hash);
                }
            }
        }