Something resembling can be got by inserting a periodic (stripe width) geometric distortion which affects only horizontally. In addition to emulate "it's made of glass, which causes also gloss and light variations" you must add a blended layer or a masked adjustment layer which generates the light variations. It must have the same repeating period as the distortion stripes.
Affinity Designer doesn't process photos, but its brother Affinity Photo has "Deformation with equations". It can create the distortion. Quite the same is available in the G'MIC filter pack which is freely available for GIMP, Krita, Paint.NET and Photoshop. In G'MIC it's named "Cartesian Transform". I have it in Krita. An example of the final result:
It has the repeating geometric distortion and light variations The image was originally an espresso cup set advertisement in a randomly found webshop.
To create just the same periodic horizontal distortion as used in your examples needs some serious knowledge and math talent. I am unfortunately only able to handle some elementaries, so I make something simple. Here's my filtering dialog:
The parameter W means the image width in pixels. The X-expression presents where the result pixel is picked from. Y=Y means no vertical changes.
The result is this:
It has no light variations. They are inserted later.
The periodic distortion is based on the simplest commonly available periodic function "sin()". Someone who knows something maybe can write a formula which approximates better your examples. Python language math expressions are available.
One thing is sure: No math distortion formula will be 100% perfect. Why? Because the effect of the glass depends radically on how far behind the glass the watched objects are. Cannot believe it? Then take an ordinary looking glass and try. That distance dependent refraction result is true for all convex lenses.
A photo contains no depth information, so there's no way to distort differently objects at different distances. Photorealistic 3D-rendering can do it if the composition is a 3D model. Forget it in Photoshop and Affinity.
Different results can be got by changing the distortion formula. Here's only for a comparison a version with increased horizontal scattering. The scattering amplitude W/30 is increased to W/20. One stripe gathers light now from 50% wider area:
The result may be good enough even without the light variations caused by the gloss of the glass. To check what the glossiness give I added the light variations as a top layer pattern of stripes which have blending mode soft light and reduced opacity. The pattern was this:
The right period was got by painting it only a little in the left and by adding the next Cartesian transform:
I only removed the +x from the expression for the x. The result was smoothed by blurring and the contrast was increased to compensate. The result after reducing the opacity and changing the blending mode to soft light the result became the same as shown in my starting image.
EDIT: The periodic distortion based on function sin() creates quite round effect. Your example and the Pilkington reed glass in my comment maybe have more prism-like stripes. The sharp step edges in the result hint to that direction. To approximate it the periodic function must have a clear discontinuity. A simple way to get it is to use the fractional part of integer division. In the next example it's (X * W/40 - int(X * W/40)). It drops to zero after every W/40 pixels: