I am searching for a way to make a blurred object in Adobe Photoshop like the image I've made in Adobe XD with the Background-Blur tool.
Here's one simple method. There may be others . . .
Create a copy of the background layer, and apply some Gaussian blur to it.
Use the elliptical selection tool to make a circle, then add it as a layer mask
Add a layer above, fill it with white, reduce the layer opacity to something like 50%, then clip it to the blurred layer below
To move the circle around, select the Move Tool and switch off Auto-Select in the tool options along the top, select the layer mask, and unlink the mask from the image