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.
uint32_t nFetchFlags = 0;
    if ((pfrom->GetLocalServices() & NODE_WITNESS) && State(pfrom->GetId())->fHaveWitness) {
        nFetchFlags |= MSG_WITNESS_FLAG;
    }
    return nFetchFlags;
}
inline void static SendBlockTransactions(const CBlock& block, const BlockTransactionsRequest& req, CNode* pfrom, CConnman* connman) {
    BlockTransactions resp(req);
    for (size_t i = 0; i < req.indexes.size(); i++) {
        if (req.indexes[i] >= block.vtx.size()) {
            LOCK(cs_main);
            Misbehaving(pfrom->GetId(), 100, strprintf("Peer %d sent us a getblocktxn with out-of-bounds tx indices", pfrom->GetId()));
            return;
        }
        resp.txn[i] = block.vtx[req.indexes[i]];
    }
    LOCK(cs_main);
    const CNetMsgMaker msgMaker(pfrom->GetSendVersion());
    int nSendFlags = State(pfrom->GetId())->fWantsCmpctWitness ? 0 : SERIALIZE_TRANSACTION_NO_WITNESS;
    connman->PushMessage(pfrom, msgMaker.Make(nSendFlags, NetMsgType::BLOCKTXN, resp));
}
bool static ProcessHeadersMessage(CNode *pfrom, CConnman *connman, const std::vector<CBlockHeader>& headers, const CChainParams& chainparams, bool punish_duplicate_invalid)