These are two different kind of insects:
There is one pair of translucent wings (admittedly, the number of wing pairs is not visible from the photo), what tells us it must be some kind of fly (Diptera).
Further, the antenna is rather short, from what we can deduce it must be a brachyceran fly.
Even further, it has three segments, so we can conclude it is a member of the family "soldier flies" (Stratiomyidae).
A friend (a dipterologist), upon seeing the photo, immediately argued it must be a "black soldier fly (Hermetia illucens), a meanwhile cosmopolitan species that has gained economic importance in organic recycling.
This one is much trickier, I think.
It does look like a shore bug (Saldidae): the large eyes, slender and long antenna and legs, the flat and oval body - everything fits.
But shore bugs are tightly bound to their habitats (shores of all kinds of waterbodies). And at least in Europe, it is very unlikely (although not impossible) to find one inside a building.
Also, shore bugs are very agile and are fast runners, jumpers and flyers - what contradicts the OP's description ("It mostly sits [...], does not move").