I was reviewing other posts where several people mentioned that the installation was getting stuck at a specific percentage. If you already tried the basic steps I mentioned in this post
There are two other possible solutions that worked for some people:
Pause and resume the installation
They paused the download in the Epic Games Launcher, waited a few seconds, and then resumed it. In some cases, this forced the launcher to reconnect properly and the installation continued.
Install an older version of the Epic Games Launcher (18.8.1)
Some users mentioned that the issue was related to the launcher version rather than Unreal itself. After uninstalling the current launcher and installing an older version (specifically v18.8.1), they were able to install the engine without it getting stuck again.