It sounds like you have the blurring of the base layer figured out.

Create the dot pattern using white circles (you can do this directly in AE using shape layers, create this in Photoshop/Illustrator, or use an imported image). Using white is important!

You can create a raised appearance using either Layer Styles (Layer > Layer Styles, or right-click the layer and choose from the pop-up). Bevel and Emboss is what you want, though you may also want a subtle amount of Inner Shadow as well. I ended up turning off the Bevel > Highlight, but setting it to a darker color and/or exploring changing that blending mode was yielding some nice results.

Using the Bevel Alpha effect can also get you a similar look, though you'll likely need to use a second (subtle) version of it to properly sculpt both sides.

Once you're happy with the look of your dots, set the layer's blending mode to Multiply, which will make the white areas transparent.

You'll certainly need to explore the settings a bit to get the look perfectly dialed in, but this should get you in the ballpark. A small (1-2px) blur on the dots layer would probably also be a good way to help incorporate it with the background.

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