[Export and reduce dpi for website images]

To "save for web" in Affinity Designer you would:

1. Select the Export Persona
2. On the layers pallete on the bottom right choose "create slices"
3. Then on the layer(s) you want to export expand them and you'll see similar options as "Save for web" in PS
4. Then simply un-check the layers you don't want (you might have duplicate slices at this point)
5. Click Export Slices (n) (where n is the number of slices selected)

[Export and reduce dpi for website images]

So to answer why PS reduces DPI when using "Save for web"...well, it doesn't.

 

PS reduces PPI (pixels per inch) which is different to DPI (dots per inch).

 

Other than than what "save for web" does is:

• optimize how much compression is used for JPEGs
• Removes unnecessary metadata
• Allow choosing if transparency should be used in PNG and what bit PNG should be (8 0r 24 I think)
• Allows choosing optimized PNGs (which load gradually and not all at once...don't see much of them anymore but remember dial-up? That kinda load experience)
• Optimize how many colors are in GIFs
• and choose image dimensions

So with those options you can certainly reduce a files size for better web results.

 

So yeah, Affinity Photo and Designer should have something like that I feel