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.
{
    CKeyMetadata meta;
    {
        LOCK(cs_wallet);
        auto it = mapKeyMetadata.find(keyID);
        if (it != mapKeyMetadata.end()) {
            meta = it->second;
        }
    }
    if (meta.has_key_origin) {
        std::copy(meta.key_origin.fingerprint, meta.key_origin.fingerprint + 4, info.fingerprint);
        info.path = meta.key_origin.path;
    } else { 
        std::copy(keyID.begin(), keyID.begin() + 4, info.fingerprint);
    }
    return true;
}
bool CWallet::AddKeyOrigin(const CPubKey& pubkey, const KeyOriginInfo& info)
{
    LOCK(cs_wallet);
    std::copy(info.fingerprint, info.fingerprint + 4, mapKeyMetadata[pubkey.GetID()].key_origin.fingerprint);
    mapKeyMetadata[pubkey.GetID()].key_origin.path = info.path;
    mapKeyMetadata[pubkey.GetID()].has_key_origin = true;
    mapKeyMetadata[pubkey.GetID()].hdKeypath = WriteHDKeypath(info.path);
    return WriteKeyMetadata(mapKeyMetadata[pubkey.GetID()], pubkey, true);
}