Coming back with good news 
First, I have replaced my current router (Sophos XG) with another one (Fortigate 30E).
Same behavior.
So this means the root cause is not the router, but something else in the network.
I have 2 only other network appliance plugged to my network, the switch and a Pi-Hole (10.0.0.249).
My eyes go to the Pi-Hole and after forcing the resolution of the name to point to the Pi-Hole, my previous tests was not good (DNS result with good value) because my DNS resolution is forwarded to other servers and the name resolution from Pi-Hole was wrong :
My bad, the previous test was not relevant.
This is very strange because the Pi-Hole entry is good:
But associated resolution was wrong … WHAT THE H*** ???
So I delete and recreate the DNS entry into the Pi-Hole and after flushdns cmd and reboot Homey, the resolution is ok :
After that, all is working like a charm and Insight come back.
To conclude, I confirm that 10-0-0-41.homey.homeylocal.com must works and point to Homey.
Thank you very much @robertklep for your help and for your time. Your focus on homeylocal url was the good resolution path, and I assume that my network environment is not “classic”, so I understand it can be difficult to troubleshoot.
My case may serve others. I share my resolution for people in case same or similar behavior.
Regards.
