There's a limit to how much can be done using the JPEG you uploaded here.... working from the original RAW would make for much better results (mostly, much more recovery of the blown out highlights).

Rather than try to fix your edited example, I tried different editing from your original. I used Photoshop to do selective editing with Layers & Masks.

1. First I created a layer that's an exaxt copy of the background. I temporarily "turned it off", in order to work on the background.

2. Next I lightened the background layer to bring up the detail in the most heavily shaded areas. Doing this overly

3. Then I turned the top/copy layer back on and reduced the exposure of that to try to recover some of the blown out highlights (there wasn't a lot I could do with the JPEG).

4. Next I created a mask on the top layer and using a "black brush" I "painted away" all but the highlight areas (the doorway, the one column and the floor at it's base). This reveals the background.

The great thing about using a mask in this way is that you can correct any mistakes simply by switching to a "white brush" and painting it back. You also can change the size, hardness versus feathtering, shape and transparency of the tool you're using to make the mask. It's possible to make gradients and blends, too. I often do those by first "painting away" an area with a black brush, then switching to a 10% or 20% white brush and painting with that for only partial recovery.

This selective adjustment is similar to what others did above, I think. The key is having the ability to separately adjust the shadow areas and the highlight areas. Both extremes are exceeding the capabilities of the camera.... and what's needed in each is the opposite of the other! In other words, the scene has a dynamic range greater than the camera can capture in a single image. These adjustments are, in effect, reducing that dynamic range to something manageable. This is what HDR tries to do. I just did it manually instead, which gives me more control over exactly where the adjustments are applied.

It's not great, but better. At least there are no halos now: