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.
{
    if (state->pindexBestKnownBlock && pindex == state->pindexBestKnownBlock->GetAncestor(pindex->nHeight))
        return true;
    if (state->pindexBestHeaderSent && pindex == state->pindexBestHeaderSent->GetAncestor(pindex->nHeight))
        return true;
    return false;
}
/** Update pindexLastCommonBlock and add not-in-flight missing successors to vBlocks, until it has
 *  at most count entries. */
static void FindNextBlocksToDownload(NodeId nodeid, unsigned int count, std::vector<const CBlockIndex*>& vBlocks, NodeId& nodeStaller, const Consensus::Params& consensusParams) EXCLUSIVE_LOCKS_REQUIRED(cs_main)
{
    if (count == 0)
        return;
    vBlocks.reserve(vBlocks.size() + count);
    CNodeState *state = State(nodeid);
    assert(state != nullptr);
    
    ProcessBlockAvailability(nodeid);
    if (state->pindexBestKnownBlock == nullptr || state->pindexBestKnownBlock->nChainWork < chainActive.Tip()->nChainWork || state->pindexBestKnownBlock->nChainWork < nMinimumChainWork) {
        
        return;
    }
    if (state->pindexLastCommonBlock == nullptr) {
        
        
        state->pindexLastCommonBlock = chainActive[std::min(state->pindexBestKnownBlock->nHeight, chainActive.Height())];
    }