Latency Test OK, dennoch Fehlermeldung

PCW, thanks for your answer!Yes, indeed. If I start the PC, my auto internet connection via RTL8111 is online but no websites reachable. eno1 connection to the Mesa card is working but with slower ping. If I switch to a faster ping with "sudo ethtool -C eno1 rx-usecs 0 ", my auto internet connection is online, but I can't reach any website as before. That's only possible if I close the eno1 connection.
I had to install lshw first. The feedback is - not the same irq for both connections.   

I just installed OBS to make a video of that phenomenon.  Maybe I do that tonight. Nope. OBS doesn't recognize my mic. I have to research.

I am shy to install this machine completely new, because I have installed several things and packets up to this point and did not document them. Beginning with libre office, Atril, Firefox, Chrome, Telegram, Geany, Visual Studio (all no problem to install again) and several packages to help with all of these Debian/LCNC problems on my way. Is there any tool or command to show me these not included packages in Debian 12? That would help me a lot.

Thank you for your time and effort...! 

Can you post the result of

ip a

Maybe  a routing/ip address issue?

Of course:

hanno@cnc2:~$ ip a
1: lo: <LOOPBACK,UP,LOWER_UP> mtu 65536 qdisc noqueue state UNKNOWN group default qlen 1000
    link/loopback 00:00:00:00:00:00 brd 00:00:00:00:00:00
    inet 127.0.0.1/8 scope host lo
       valid_lft forever preferred_lft forever
    inet6 ::1/128 scope host noprefixroute
       valid_lft forever preferred_lft forever
2: enp2s0: <BROADCAST,MULTICAST,UP,LOWER_UP> mtu 1500 qdisc fq_codel state UP group default qlen 1000
    link/ether 00:0a:cd:00:00:56 brd ff:ff:ff:ff:ff:ff
    inet 192.168.178.55/24 brd 192.168.178.255 scope global dynamic noprefixroute enp2s0
       valid_lft 855370sec preferred_lft 855370sec
3: eno1: <BROADCAST,MULTICAST,UP,LOWER_UP> mtu 1500 qdisc fq_codel state UP group default qlen 1000
    link/ether 00:23:24:5b:b4:ac brd ff:ff:ff:ff:ff:ff
    altname enp0s25
hanno@cnc2:~$

Tonight, I thought by myself - maybe it's a stroke of fate, that just one connection in time  is working correctly. I would never surf the internet while running my router. In real operation, I will need internet just for updates, research, nothing really worth. BUt technically, I think that should work, and in your simulation it ran free of problems. So, I would go on...
Thanks for your time!
Hanno
 

So eno1 does not have an assigned IP address

What does /etc/network/interfaces contain?

cat /etc/network/interfaces
 

Well, that was at the time as I cut the MEesa eno1 connection in purpose to be in internet and coming into the forum to write my post.
Eno1 has a fixed IP in network manager:  10-10-10-10 MEsa resp. -2 for Intel Card.
The connection eno1 does not have an ip adress in that state. Here is an ip a with both states. Upper feedback is with connection active, lower lines without.

 

Content of /interfaces is commented out except the loopback:
 

Just a guess but you definitely  do _not_ want a gateway (or DNS) 
address on the 10.10.10.x range

I have another idea. Maybe you can save your /etc/network/interfaces file and paste this one.
then open 2 tabs of terminal. In the first you run "sudo journalctl -f"
the system log and in the second "sudo systemctl restart networking.service". then we should see what's going on. Alternatively you can also use "sudo journalctl -f >log.txt". Then the output will be written straight into the log.txt file and you can post it.
the last step would be to delete the connections in the network manager first.

i found this here forum.linuxcnc.org/9-installing-linuxcnc...esa-ethercat?start=0
It seems rod was in trouble but not sure how he fix it.

 PCW, Tommylight: I deleted the 10.10.10.1 gateway entry and the "IPV4 Addressierung". Both has no effect for the connections.
Chris(at)cnc: I tried your interfaces file - after restart I have no connections anymore.

So, I think I should give it up. I go with the status quo and start with manually configured connections as before, in network manager.
I would like to have a starter file on my desktop, with the ethtool line.
Can you help me to create that batch with sudo ethtool -C eno1 rx-usecs 0 ? I created a file called ethtool.sh, but I can't start it with double-click.
Then, I created a starter file with  Exec=konsole --hold -e bash /home/hanno/Schreibtisch/ethtool.sh but that doesn't work. I found that line in a forum posting but I dont have the slightest idea from that...

Thanks for all your help!
Hanno