Is there any full node software for bitcoin with serious wallet functionality? I'm looking for a bitcoin software with a full-featured wallet functionality and running a full node, but I cannot find any.

Bitcoin Core does run a full node and the network capabilities are great, but the wallet functionality is very limited, it does not support BIP39 mnemonic (so there is no easy way to store the private key on paper for security), the addresses are stored on disk without encryption (it does encrypt private keys, but only that). So any backup have all this data.

On the other hand, electrum wallet seems to support everything, but it connects to electrum nodes only (it does not connect to the bitcoin network) and it send public address there to query for transactions.

Is there any alternative I'm missing? I thing that any sofware that make the wallet side of the equation while connecting to the full node I'm already running should work, but could not find any thin client wallet for bitcoin.
You can connect your Electrum wallet to your own Electrum server to preserve privacy. There are different Electrum server implementations:


Electrum Personal Server


  Electrum Personal Server aims to make using Electrum bitcoin wallet more secure and more private. It makes it easy to connect your Electrum wallet to your own full node.

ElectrumX - Reimplementation of electrum-server


  A reimplementation of Electrum-Server for a future with bigger blocks.

electrs - Electrum Server in Rust


  The motivation behind this project is to enable a user to run his own Electrum server, with required hardware resources not much beyond those of a full node.