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.
{
    LOCK(cs_wallet);
    assert(m_max_keypool_index < std::numeric_limits<int64_t>::max()); 
    int64_t index = ++m_max_keypool_index;
    if (!batch.WritePool(index, CKeyPool(pubkey, internal))) {
        throw std::runtime_error(std::string(__func__) + ": writing imported pubkey failed");
    }
    if (internal) {
        setInternalKeyPool.insert(index);
    } else {
        setExternalKeyPool.insert(index);
    }
    m_pool_key_to_index[pubkey.GetID()] = index;
}
bool CWallet::ReserveKeyFromKeyPool(int64_t& nIndex, CKeyPool& keypool, bool fRequestedInternal)
{
    nIndex = -1;
    keypool.vchPubKey = CPubKey();
    {
        LOCK(cs_wallet);
        if (!IsLocked())
            TopUpKeyPool();
        bool fReturningInternal = fRequestedInternal;
        fReturningInternal &= (IsHDEnabled() && CanSupportFeature(FEATURE_HD_SPLIT)) || IsWalletFlagSet(WALLET_FLAG_DISABLE_PRIVATE_KEYS);
        bool use_split_keypool = set_pre_split_keypool.empty();