Is there any full node software for bitcoin with serious wallet functionality?
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.