How does electrum interact with the underlying bitcoind service?
Electrum Server is a fancy abstraction on top of bitcoind and a custom index of UTXO data. Client wallets connect to it and send queries for details about their wallet, using its own index Electrum Server requests the correct information from bitcoind and returns it to the client. The Electrum Server keeps its index up to date by continuously querying bitcoind for changes such as mempool updates or new blocks.

All communication with the wider Bitcoin network happens through bitcoind, including block updates and transaction broadcasts. For the purpose of this discussion, Electrum servers are standalone and completely unaware of one another, there is no cross communication between them.