Nearly all essentials are already said by others, but a little more can still be inserted.
At first: if it's not colored to blue it shouldn't be blue. Gold and copper are yellow or red but steel and aluminium should be neutral.That means all color they have is reflected from the environment.
Let's assume it's made of neutral metal. How it reflects the environment (including the lights) depends on the curvature and the smoothness of the surface. If it was a perfect plane having all grains smaller than 100 nanometers it would be a mirror. You might have something like this:
Nobody has suggested it, no matter it's quite obvious. That's because it's too obvious and would very likely be seen as catty sophistry. It would depend fully on the mood of the moderator how long one's account would stay closed. So, I skip it, too.
Let's start from an uniformly 50% grey piece and let it get gradually more light and reflections:
It's more like painted on the wall. It's too dark to be plain metal and its color is anything but neutral when compared to the appearance of the background. The simplest way to make it more metallic is to change the fill color to a gradient which is in harmony with the background lightness reduction from left to right. No detailed environment reflections are needed if we let it look planar but matt. The colors must be taken from the background photo. otherwise it will not look uncolored neutral metal.
I have a spare copy of the artwork. I used it to make a new version. I clicked by holding Ctrl the image icon in the Layers panel to make a perfect selection and filled with a gradient the selection in layer Artwork. (See NOTE1)
The gradient start and stop colors were picked from the background wall. The curves layer was inserted on the top to lift up the brightness. Note: The next layer only switch is ON and the curve is 45 degrees tilted straight line, only lifted the ends upwards to insert brightness but not changing the apparent material color (see NOTE2)
It's still like it's painted on the wall. Layer style Bevel&Emboss gives some apparent thickness:
That simply makes the edge areas lighter (=white with blending mode screen) on the sunny side and the shadow side edges are made darker (=black with blending mode multiply). The original colors must be far enough from white and black to allow the effect.
Layer style Drop Shadow creates apparent gap between the wall and the artwork as you probably already knew:
You have in the left a weak lamp which seemingly is strong enough to colorize the wall in the shadow near the lamp. The same redness doesn't exist in other shadows. Thus I didn't insert it to my effects. If the same redness were in all shadows it should be used also in the effects. I would remove the the whole lamp or at least edit the shadow to the same color as other shadows.
Bevel&Emboss with weird settings can create fake curved surface and fake chrome-like glossy reflections:
The blending modes are changed to Normal for better control. Pure black isn't good on your brownish background photo, so I changed the shadow color in the Bevel&Emboss dialog to dark brown. The beveling curve is changed to contain a partial grayscale inversion (=the common metallization trick, can be used also with curves in a BW image)
Bevel&Emboss with weird settings create difficult to predict results. Prepare to make numerous attempts and there's no guarantee you'll find anything useful.
As another example a partially transparent flat version is added to reduce the excessive effect of weird settings. Its moved a little to 4 o'clock:
NOTE1: As well you could keep the original fill color and insert the gradient as a layer style. Layer style Gradient Overlay is as good as gradient fill color if you set the blending mode to normal in Layer Style editing dialog. Even the brightening adjustment layer (=curves) could be omitted if you inserted a grey color overlay layer style with blending mode Add.
NOTE2: If one looks for ex. this ad https://www.oregometal.com/aluminium-color-anodizing/ your original blue version starts to look possible. If it happens that you plan to give an electrochemical treatment to your artwork for a certain surface look (=color, shiny graininess) you should have a piece of the treated material. Shoot a photo of it with the real background and light and pick the colors for your mockup from it.
Your brownish low color temperature light cannot show properly bright colors. You should have high color temperature light or at least you should try to fix the white balance (no guarantee it makes the colors right due the sparse spectrum of many modern low cost but bright lamps, use studio lamps to be sure)
Just for testing I made a version where the background image white balance is corrected, the saturation is lifted up and the artwork has a weird bevel&emboss with colors borrowed from the mentioned anodized aluminium advertisement.
Now it has a realistic blue color, but I'm afraid I have dropped out the good taste in some phase.