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.
is up-to-date.  With a non-empty response, we can initialise
                   the peer's known best block.  This wouldn't be possible
                   if we requested starting at pindexBestHeader and
                   got back an empty response.  */
                if (pindexStart->pprev)
                    pindexStart = pindexStart->pprev;
                LogPrint(BCLog::NET, "initial getheaders (%d) to peer=%d (startheight:%d)\n", pindexStart->nHeight, pto->GetId(), pto->nStartingHeight);
                connman->PushMessage(pto, msgMaker.Make(NetMsgType::GETHEADERS, chainActive.GetLocator(pindexStart), uint256()));
            }
        }
        
        
        
        {
            
            
            
            
            
            
            
            LOCK(pto->cs_inventory);
            std::vector<CBlock> vHeaders;
            bool fRevertToInv = ((!state.fPreferHeaders &&
                                 (!state.fPreferHeaderAndIDs || pto->vBlockHashesToAnnounce.size() > 1)) ||
                                pto->vBlockHashesToAnnounce.size() > MAX_BLOCKS_TO_ANNOUNCE);
            const CBlockIndex *pBestIndex = nullptr; 
            ProcessBlockAvailability(pto->GetId()); 
            if (!fRevertToInv) {
                bool fFoundStartingHeader = false;