Chromium for Android does not support Extensions, and never have.
Attempting to enable it would require hundreds, if not thousands, of individual patches that have to be maintained (we know, we tried, and gave up after several months).
AFAIK the Kiwi dev did do that task, but the dev has apparently not been able to update the chromium version for quite a while, probably because there are too many changes in the relevant code.
As for Edge, my guess is that they developed their own support for it from scratch (not based on the Chromium desktop code), which probably means there are compatibility issues with existing desktop extensions.