I've tried my best, but failed to remove or at least somehow blend the light of the spotlight in the left upper corner. What is the best approach to do it (using Photoshop/Lightroom)?
In LR, you can roughly select the area (generously), and simply reduce Highlights and Whites. In PS, there are many more sophisticated methods that you could apply.
Note that all you can ever achieve is to leave the area inconspicuous and blended in with the background; you cannot recover what was 'under' the spotlight as it was overwritten when taking the photo.
I don't see a "spotlight" in the left-upper corner. There is a blown-out area at the top of the frame, left of center. Since it is blown out, there is pretty much nothing you can do to "fix" it.
You can try something like content-aware infill, but results are unpredictable.
To avoid similar problems in the future, reposition the camera so that unwanted elements are not contained within the frame.
Try Photoshop Levels with a mask. It basically allows to apply Levels to only selected areas of the photo. You can create the mask image first as another layer with black background and paint a white fuzzy ellipse over the spotlight, then copy this layer into the layer mask. Then play with the Levels sliders to make it darker. It is also possible to apply the mask with other filter-layers, e.g. saturation etc.
Search YouTube for [photoshop mask level]. There are many tutorials how to do it.
Well. I am with @Mike Taylor on this one.
If you can not fight them, join them. As it is now, yes, the flare looks distracting because it is an element not integrated with the rest of the scene.
One aspect of a photo, depending on the usage, is to capture a "mood" and ambient, an idea. In this case, the flare is part of it. I would use it to my advantage, probably adding some special effects... an additional lens flare. (Many programs have this type of filters)