sorry for the late reply, did not look into this topic for a long time...
with latest updates (bullseye) lspci recognizes the adapter:
Ethernet controller: Realtek Semiconductor Co., Ltd. RTL8125 2.5GbE Controller (rev 05)
uname -a
5.15.39-3-pve #2 SMP PVE 5.15.39-3 (Wed, 27 Jul 2022 13:45:39...