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.
{
    const CTransaction& tx = *ptx;
    {
        AssertLockHeld(cs_wallet);
        if (!block_hash.IsNull()) {
            for (const CTxIn& txin : tx.vin) {
                std::pair<TxSpends::const_iterator, TxSpends::const_iterator> range = mapTxSpends.equal_range(txin.prevout);
                while (range.first != range.second) {
                    if (range.first->second != tx.GetHash()) {
                        WalletLogPrintf("Transaction %s (in block %s) conflicts with wallet transaction %s (both spend %s:%i)\n", tx.GetHash().ToString(), block_hash.ToString(), range.first->second.ToString(), range.first->first.hash.ToString(), range.first->first.n);
                        MarkConflicted(block_hash, range.first->second);
                    }
                    range.first++;
                }
            }
        }
        bool fExisted = mapWallet.count(tx.GetHash()) != 0;
        if (fExisted && !fUpdate) return false;
        if (fExisted || IsMine(tx) || IsFromMe(tx))
        {
            /* Check if any keys in the wallet keypool that were supposed to be unused
             * have appeared in a new transaction. If so, remove those keys from the keypool.
             * This can happen when restoring an old wallet backup that does not contain
             * the mostly recently created transactions from newer versions of the wallet.
             */