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.
uint64_t nCMPCTBLOCKVersion = (pfrom->GetLocalServices() & NODE_WITNESS) ? 2 : 1;
            if (lNodesAnnouncingHeaderAndIDs.size() >= 3) {
                
                
                connman->ForNode(lNodesAnnouncingHeaderAndIDs.front(), [connman, nCMPCTBLOCKVersion](CNode* pnodeStop){
                    AssertLockHeld(cs_main);
                    connman->PushMessage(pnodeStop, CNetMsgMaker(pnodeStop->GetSendVersion()).Make(NetMsgType::SENDCMPCT, false, nCMPCTBLOCKVersion));
                    return true;
                });
                lNodesAnnouncingHeaderAndIDs.pop_front();
            }
            connman->PushMessage(pfrom, CNetMsgMaker(pfrom->GetSendVersion()).Make(NetMsgType::SENDCMPCT, true, nCMPCTBLOCKVersion));
            lNodesAnnouncingHeaderAndIDs.push_back(pfrom->GetId());
            return true;
        });
    }
}
static bool TipMayBeStale(const Consensus::Params &consensusParams) EXCLUSIVE_LOCKS_REQUIRED(cs_main)
{
    AssertLockHeld(cs_main);
    if (g_last_tip_update == 0) {
        g_last_tip_update = GetTime();
    }
    return g_last_tip_update < GetTime() - consensusParams.nPowTargetSpacing * 3 && mapBlocksInFlight.empty();
}
static bool CanDirectFetch(const Consensus::Params &consensusParams) EXCLUSIVE_LOCKS_REQUIRED(cs_main)
{
    return chainActive.Tip()->GetBlockTime() > GetAdjustedTime() - consensusParams.nPowTargetSpacing * 20;
}
static bool PeerHasHeader(CNodeState *state, const CBlockIndex *pindex) EXCLUSIVE_LOCKS_REQUIRED(cs_main)