The closest official replacement would be one of the Arduino MKR boards (MKRZERO is a good choice) with the MKR ETH Shield. I realize that's not exactly what you're looking for since it's not a single board, but it is smaller than your Arduino Ethernet (though a bit taller). Often, you will find that Arduino code will work with one of the modern SAMD boards as well as the classic AVR boards but in some cases you will find libraries or sketches that contain architecture-specific code and requires modifications to work on another architecture.