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.
ConsiderEviction(pto, GetTime());
        
        
        
        std::vector<CInv> vGetData;
        if (!pto->fClient && ((fFetch && !pto->m_limited_node) || !IsInitialBlockDownload()) && state.nBlocksInFlight < MAX_BLOCKS_IN_TRANSIT_PER_PEER) {
            std::vector<const CBlockIndex*> vToDownload;
            NodeId staller = -1;
            FindNextBlocksToDownload(pto->GetId(), MAX_BLOCKS_IN_TRANSIT_PER_PEER - state.nBlocksInFlight, vToDownload, staller, consensusParams);
            for (const CBlockIndex *pindex : vToDownload) {
                uint32_t nFetchFlags = GetFetchFlags(pto);
                vGetData.push_back(CInv(MSG_BLOCK | nFetchFlags, pindex->GetBlockHash()));
                MarkBlockAsInFlight(pto->GetId(), pindex->GetBlockHash(), pindex);
                LogPrint(BCLog::NET, "Requesting block %s (%d) peer=%d\n", pindex->GetBlockHash().ToString(),
                    pindex->nHeight, pto->GetId());
            }
            if (state.nBlocksInFlight == 0 && staller != -1) {
                if (State(staller)->nStallingSince == 0) {
                    State(staller)->nStallingSince = nNow;
                    LogPrint(BCLog::NET, "Stall started peer=%d\n", staller);
                }
            }
        }
        
        
        
        auto& tx_process_time = state.m_tx_download.m_tx_process_time;
        while (!tx_process_time.empty() && tx_process_time.begin()->first <= nNow && state.m_tx_download.m_tx_in_flight.size() < MAX_PEER_TX_IN_FLIGHT) {
            const uint256& txid = tx_process_time.begin()->second;
            CInv inv(MSG_TX | GetFetchFlags(pto), txid);