Starship Troopers: Extermination has used Epic Online Services (EOS) since the early access launch. For example we rely on Epic Online Services for anti-cheat functionality, player reporting and moderation in our game.

This connection has become more visible in the 0.5.2 update, as we released the game on the Epic Games Store. In order to allow Steam and Epic players to invite each other into parties, the Epic “Social Overlay” needs to be used. Epic, or any other distribution platform, cannot access the Steam friends list, it is only available for Steam players. The Epic overlay, however, is available for any distribution platform. For the Steam version, we decided to keep the cross-platform Epic overlay side by side with the native Steam friends overlay.
The installer is required for the Epic "Social Overlay" to function. The game was already previously installing multiple prerequisites at startup (Epic Anti-Cheat services, C++ redistributables etc).
No, the Epic Games Store is not tied to the Epic “Social Overlay”. The game on Steam will not install the Epic Games Store. The Steam version of Starship Troopers: Extermination does not require the Epic Games Store / Launcher application to function.
You can, but you will lose the ability to add friends outside the Steam network, to invite non-Steam players to the game, or to be invited by non-Steam players. If you manually uninstall any required services, you may have to reinstall them later to restore the cross-platform invite functionality.