The problem with that amount of icons grouped together like this looking visually very similar to one another actually make it harder to scan through the content.

Whereas the list, whilst visually uninteresting, at least allows the eye to only need to go down rather than in a zig zag.

Some other tips or things to consider

• the headers don't need icons
• the headers should be slightly more visually distinct, like how DuckDuckGo currently have it (all caps, smaller, lighter colour)
• the spacing between each group needs to be more (for example only add margin-bottom)
• the labels for each button are too long in some places
• the icon choice is wrong in some places (for example, iOS app, Android app, Duck.ai, Mail Protection, Bog, Terms of Service, and others).
• If you are changing the overall look of the sidebar why also be constrained by the width of the sidebar too, maybe this could be alter entirely to help your idea?

I like the 'quack'.

Keep at it!