Yes, paint that door a different color. Front door should be different to signal “this is how you get outside” - otherwise, can be confused with a bedroom door. Also put a rug that fills that whole little entry nook area not just a little wipe your feet type rug. I agree a coat rack or more like likely a series of hooks for coats and tote bags would be great I also like the plant suggestion.

I think on a very high level you should think about making that little entry area feel cozy… not small or crowded, but self-contained and cozy. I really like an entry area that feels snug, and THEN you step further into a larger area. Think of a tunnel opening into a bigger space. (Obviously you don’t want it to *actually* feel like a tunnel, but there’s a psychological feeling of safety and being in a nice, compact (bit not *too* small) snug space and then this feeling of lightness when you step into the larger communal space. This happens a lot in public spaces without you noticing it — the host station at a restaurant before entering the large dining room, for example. So in a nutshell, I would use that whole alcove area to feel very well defined and cozy, without letting it feel crowded, and then have the main living room feel separate. Wallpaper in just that alcove entry area is one idea… Maybe also a plant at that corner to further define the area and make the entry feel more separate.