Screaming Frustration

[Blighty]

You want an image 16 x 16 inches.
A good quality print is 300 dpi (dots per inch, or pixels per inch)
So 16 x 16 inches is (16 * 300) x (16 * 300) pixels
= 4800 x 4800 pixels.
Find a background that size (in pixels !)

Your image has only one layer. You need to work with layers.

Your image has a white background which is 3840 x 2160 pixels
This can be seen in the title bar at the top of the Gimp window.
If you look at the ruler you can see that this white background is 40 x 22 inches
You can see that your pattern is much smaller than the white background

Your background pattern is pasted into the white background. MISTAKE !
Your background pattern should be on its own layer
Edit > Paste As > New Layer
You can see this in the Layers Dialogue.
You can see that your pattern is much smaller than the white background. Gimp is showing it correctly.

The Scale Tool scales the entire layer, in this case the white background with your pattern on it.
If your pattern was on its own layer it could be scaled independently.

Bitmap images do not scale well. It introduces blurring. The greater the amount of scaling, the greater the blurring.
In your case your background image is much too small to scale to the size you want.