There is a newer image in backports, I installed version:
# apt list --installed | grep linux-image.*back
linux-image-6.5.0-0.deb12.4-amd64/stable-backports,now 6.5.10-1~bpo12+1 amd64 [installed]

After reboot version changed:
# uname -a
Linux P7730 6.5.0-0.deb12.4-amd64 #1 SMP PREEMPT_DYNAMIC Debian 6.5.10-1~bpo12+1 (2023-11-23) x86_64 GNU/Linux

And problem (when connecting cable network) is gone, network and Gnome work as usual :-)

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