Hi, @ldez,
Thanks for your input.
The root of my problem isn't with the fact that domains point to different IPs, that was done on my side while I was trying to figure out the reasons behind the behavior.
The problem is in cloudflare processing .com and .me domains differently, for whatever reason. When I disabled its features for .me domain (the reason you see a different IP address), Traefik started routing the traffic properly to the app.
.com still has the SAME set of features ENABLED, yet the app is working just fine.
I have tried to troubleshoot cloudflare previously, but disabling its protection and other features yielded no results. That is why I was thinking Traefik is the root of this behavior.
This time it worked, so I am finally relieved of this headache.
Thanks to @cakiwi, I've learned that curl has a parameter --resolve, which helped me to look in the right direction.
I am not able to close the topic, so if you can do it, please go ahead and do so.