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.
{
    AssertLockHeld(cs_main);
    if (chainActive.Contains(pindex)) return true;
    return pindex->IsValid(BLOCK_VALID_SCRIPTS) && (pindexBestHeader != nullptr) &&
        (pindexBestHeader->GetBlockTime() - pindex->GetBlockTime() < STALE_RELAY_AGE_LIMIT) &&
        (GetBlockProofEquivalentTime(*pindexBestHeader, *pindex, *pindexBestHeader, consensusParams) < STALE_RELAY_AGE_LIMIT);
}
PeerLogicValidation::PeerLogicValidation(CConnman* connmanIn, BanMan* banman, CScheduler &scheduler, bool enable_bip61)
    : connman(connmanIn), m_banman(banman), m_stale_tip_check_time(0), m_enable_bip61(enable_bip61) {
    
    recentRejects.reset(new CRollingBloomFilter(120000, 0.000001));
    const Consensus::Params& consensusParams = Params().GetConsensus();
    
    
    
    
    static_assert(EXTRA_PEER_CHECK_INTERVAL < STALE_CHECK_INTERVAL, "peer eviction timer should be less than stale tip check timer");
    scheduler.scheduleEvery(std::bind(&PeerLogicValidation::CheckForStaleTipAndEvictPeers, this, consensusParams), EXTRA_PEER_CHECK_INTERVAL * 1000);
}
/**
 * Evict orphan txn pool entries (EraseOrphanTx) based on a newly connected
 * block. Also save the time of the last tip update.
 */
void PeerLogicValidation::BlockConnected(const std::shared_ptr<const CBlock>& pblock, const CBlockIndex* pindex, const std::vector<CTransactionRef>& vtxConflicted) {