Ethernet
The wired port (PCI ID 104d:9104) is handled by the mts driver, which every PS5 kernel builds and loads by itself. Plug in a cable and the connection is there; nothing here is required for a normal setup.
Background
The controller is a MediaTek Star Ethernet MAC (mtk_star_emac) inside the console's Salina chip. The mts driver was written for the PS5 on top of an earlier community base and is part of the PS5 patch set, built as a module:
CONFIG_MTS=m
The interface doesn't come up
If the interface doesn't come up after the first boot, disable and re-enable the wired connection in your network manager.
USB Ethernet adapters keep disconnecting
A USB Ethernet adapter that connects and disconnects in a loop is a driver problem of that adapter, not of the console, and there is no fix beyond another adapter or cable. The internal port works on every supported firmware, so use it where you can. For a new adapter, choose one with the RTL8156B chipset.
Slow speed, high CPU use and no IPv6 on old kernels
Early versions of mts had three faults: the port topped out around 300 Mbps while a USB adapter on the same cable did full gigabit, one CPU core sat at 100%, and incoming IPv6 didn't work. All three came from the interrupt and filter setup. The interrupt mask was written with the wrong polarity and interrupts were only partly acknowledged, so the status bits stayed set, the MSI stopped firing and the driver fell back to polling every 10 ms; and the multicast filter was never programmed, so neighbour discovery and router advertisements were dropped.
The current driver matches what Sony's own does: correct mask polarity, full interrupt acknowledgement, the same interrupt moderation timer, a hash-based multicast filter with promiscuous mode, and NAPI stopped before DMA on shutdown. It does full gigabit in both directions at around 13% of one core, gets a global IPv6 address through router advertisements, and shows RX drop and CRC counters in ip -s -s link.
Every current kernel: the upstream packages, rmuxnet's kernel and PS5 Bazzite Deck, see Kernel setup. On an old kernel, update, or use a USB adapter for full gigabit speed.