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 (std::set<uint256>::iterator it = pto->setInventoryTxToSend.begin(); it != pto->setInventoryTxToSend.end(); it++) {
                    vInvTx.push_back(it);
                }
                CAmount filterrate = 0;
                {
                    LOCK(pto->cs_feeFilter);
                    filterrate = pto->minFeeFilter;
                }
                
                
                CompareInvMempoolOrder compareInvMempoolOrder(&mempool);
                std::make_heap(vInvTx.begin(), vInvTx.end(), compareInvMempoolOrder);
                
                
                unsigned int nRelayedTransactions = 0;
                LOCK(pto->cs_filter);
                while (!vInvTx.empty() && nRelayedTransactions < INVENTORY_BROADCAST_MAX) {
                    
                    std::pop_heap(vInvTx.begin(), vInvTx.end(), compareInvMempoolOrder);
                    std::set<uint256>::iterator it = vInvTx.back();
                    vInvTx.pop_back();
                    uint256 hash = *it;
                    
                    pto->setInventoryTxToSend.erase(it);
                    
                    if (pto->filterInventoryKnown.contains(hash)) {
                        continue;
                    }
                    
                    auto txinfo = mempool.info(hash);