The 2 Droyne worlds are not a threat to the 11,000 world Imperium unless the Droyne have impacted all the colonization in neighboring worlds through Psionics across multiple parsecs. There are many worlds with Amber zone.
And not politically controlling District 268 and buffering the Imperium in 5 Sisters makes some sense.
The research station is probably working on the Droyne problem instead of blasting them flat. Stephen is more peaceful than some of the predecessors. The situation lacks a lot of basic information. For example, Do the Droyne have an Ancient warship as well? It is an easy assumption, expansion stopped from the Frontier Wars and treaties not the Droyne road bump.
Grandfather.
Some in the Imperium know about Grandfather, or at least the idea of a very powerful race/being that is tied to the Droyne. They have seen whole systems destroyed by Grandfather and his war and they don't want any part of it. They don't want anyone accidentally ticking off Grandfather. They don't want any of Grandfathers little toys getting into anyone hands (except their own). They don't want the Droyne developing faster then normal and becoming a threat. Basically, as I see it, it is in the best interest of the 3I to keep the Droyne and everyone else separate.
-Just My Thougths