TL;DR: Reinstall Windows.
As many others, I had a lag/freeze (~3s) after someone reaches a new age.
If I recall correctly, it started around September 2020. I really wanted to play the game and tried a lot, but nothing really helped.
In the recent updated it was stated that the issue had been fixed, but it was not for me.
For some reason I was scrolling through my Windows Updates, and I saw that a “Functional Update” was installed around that time, and I figured, maybe thats the problem. I reinstalled Windows via the system recovery (keep personal data option) over night. I just installed Steam and AoE. The game loads MUCH quicker than before and the “age up” freeze is barely noticable (0.1s). I have no idea if it was the update that cased the issue or some other stuff that got uninstalled, but it got fixed for me.
Hope this helps someone.