Had something similar in my old flat in Lochee, kept catching it in my peripheral vision right at the end of the hall near the bathroom door. Never straight on, always just out of frame. Classic shadow person behaviour honestly.
Did you notice any temperature drop before it showed up? That's the first thing I'd want to rule out - infrasound and cold spots together usually point toward something more concrete than just a residual haunting. Also what time of night roughly? There's a pattern with these things appearing between 2-4am that keeps coming up in the literature and I've seen it firsthand too.
Have you got any photos or were you too spooked to grab your phone? No judgement either way, I've frozen up myself. But if it happens again seriously try to get something, even a blurry shot is better than nothing for ruling out mundane explanations.
What's the history of the property like?