I had tested the module with the reset problems again and it works with the current nightly build kernel (6.6.62-ipfire)
Bus 004 Device 003: ID 0b95:1790 ASIX Electronics Corp. AX88179 Gigabit Ethernet
DRIVER=ax88179_178a
MODALIAS=usb:v0B95p1790d0100dcFFdscFFdp00icFFiscFFip00in00
Settings for green0:
Supported ports: [ TP MII ]
Supported link modes: 10baseT/Half 10baseT/Full
100baseT/Half 100baseT/Full
1000baseT/Half 1000baseT/Full
Supported pause frame use: No
Supports auto-negotiation: Yes
Supported FEC modes: Not reported
Advertised link modes: 10baseT/Half 10baseT/Full
100baseT/Half 100baseT/Full
1000baseT/Full
Advertised pause frame use: No
Advertised auto-negotiation: Yes
Advertised FEC modes: Not reported
Link partner advertised link modes: 10baseT/Half 10baseT/Full
100baseT/Half 100baseT/Full
1000baseT/Full
Link partner advertised pause frame use: No
Link partner advertised auto-negotiation: Yes
Link partner advertised FEC modes: Not reported
Speed: 1000Mb/s
Duplex: Full
Auto-negotiation: on
Port: MII
PHYAD: 3
Transceiver: internal
Supports Wake-on: pg
Wake-on: d
Current message level: 0x00000007 (7)
drv probe link
Link detected: yes
also the ethtools output looks correct.