I looked at the datasheet of a random modern Ethernet chip (ENC28J60) and it's simpler than I expected, doing much less than the old Intel chip, although it includes the low level "PHY" circuitry, which was a separate Intel chip in the olden days. I expect that the newer chip has things like 10-bit counters, but they would be implemented with standard cell logic (i.e. computer-generated layout of gates) rather than the hand-optimized circuitry of the Intel chip.
On the other hand, you can get a chip like the W5300 which includes the whole TCP/IP stack along with ARP and ICMP, presumably running on an internal microcontroller.
High end NICs like Mellanox ConnectX are probably more similar to the 82586 in terms of breadth of functionality.
They have (R)DMA, hardware timestamping, encryption, etc. Although, I wouldn’t expect to see much hand crafted logic design outside of the very high speed signal paths like in the serdes.
On the other hand, you can get a chip like the W5300 which includes the whole TCP/IP stack along with ARP and ICMP, presumably running on an internal microcontroller.
https://ww1.microchip.com/downloads/aemDocuments/documents/O...
https://www.wiznet.io/wp-content/uploads/wiznethome/Chip/W53...