There are not many guides to how to best Upgrade Lineage + microG to “like” /e/, but as /e/ is not working correctly on this device the following thread which at first sight is not exactly on your subject might give some clues on what to install first. Many apps I think you will do better to install the upstream app yourself. Of course you can log in to your /e/ Browser, but not sync with the cloud. It has been found that you do need a certain minimum of sideloaded /e/ apps to get your cloud to work correctly.
When I tried to sideload Advanced Privacy on an own build without it, it failed with some security breach, try by all means, but perhaps leave it till last!