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.
state->pindexLastCommonBlock = LastCommonAncestor(state->pindexLastCommonBlock, state->pindexBestKnownBlock);
    if (state->pindexLastCommonBlock == state->pindexBestKnownBlock)
        return;
    std::vector<const CBlockIndex*> vToFetch;
    const CBlockIndex *pindexWalk = state->pindexLastCommonBlock;
    
    
    
    int nWindowEnd = state->pindexLastCommonBlock->nHeight + BLOCK_DOWNLOAD_WINDOW;
    int nMaxHeight = std::min<int>(state->pindexBestKnownBlock->nHeight, nWindowEnd + 1);
    NodeId waitingfor = -1;
    while (pindexWalk->nHeight < nMaxHeight) {
        
        
        
        int nToFetch = std::min(nMaxHeight - pindexWalk->nHeight, std::max<int>(count - vBlocks.size(), 128));
        vToFetch.resize(nToFetch);
        pindexWalk = state->pindexBestKnownBlock->GetAncestor(pindexWalk->nHeight + nToFetch);
        vToFetch[nToFetch - 1] = pindexWalk;
        for (unsigned int i = nToFetch - 1; i > 0; i--) {
            vToFetch[i - 1] = vToFetch[i]->pprev;
        }
        
        
        
        
        for (const CBlockIndex* pindex : vToFetch) {
            if (!pindex->IsValid(BLOCK_VALID_TREE)) {
                
                return;