OK, a couple of comments from your last report (but please first finish the previous test / steps, that could be enough to find the solution).
About using the original removal utilities (for Avast and for TrendMicro respectively), I would tend to think that the developers of those original security tools should know better than the users about what exactly needs to be removed. So IMO, it is not the same to run those removal utilities (developed by the developers of the security tools they remove) using the original instructions, than, for example, running CCleaner or Revo Uninstaller.
Moreover, for removing Avast for example, I *know* there are remnants that CCleaner might find even after running the specific removal utility, but I also know that those remnants are created by Windows, not by Avast, so they are not going to conflict with any other security tool I may want to install. I would suspect that something similar happens with other specific removal utilities for security tools.
The second aspect I would like to mention is that of "uninstalling features / programs / whatever" from Windows because you don't use it. Since you are troubleshooting, and you are still thinking about a complete re-installation of Windows (or at least, that was my impression), I would do it the other way around. I mean, after the re-installation of Windows, reboot and apply Windows Updates again and again with reboots in between, including the validation of your installation.
Once all Windows updates are applied and Windows is validated, reboot once more, uninstall TrendMicro under windows Safe Mode and follow the appropriate instructions so to run the removal utility for your specific version of TrendMicro. It is important to read their instructions in their website.
Besides TrendMicro, leave untouched the other tools / programs / features. Don't uninstall them. In ultimate case, you can uninstall them after the problem is finally solved.
Now, one aspect that I mentioned before is the potential corruption of your license. Since you say it starts working at first glance, and only then something happens, I would tend to think that the license is correct. But still, you should check for other types of corruption. One is hardware: you HDD where you install Windows and Avast.
The other is the filesystem itself. By uninstalling some features of windows, "something" might be happening. For example, even after 13 years, MS refuses to "completely" separate Windows (Explorer) from Internet Explorer. So the same could be happening with the network drivers or some other basic part of your OS / connection that turns into Avast updates failing.
Here the firewall rules and general configuration might have some part in this issue, together with some network drivers. BTW, since you are re-installing Windows (this weekend or anew), update the driver too.
And I am not forgetting the license itself. You could ask for a new license (with the same date), if anything else won't solve the problem. Since you said the license is not having problem at first glance, this doesn't seem to be the solution either, but we never know until we try.