The icons are not from Microsoft Teams. It's the Fluent System Icons (https://github.com/microsoft/fluentui-system-icons) free iconset by Microsoft, which Nheko (Komai's predecessor) also used and we continue to use. Because we found this iconset lacking in certain aspects, in Komai we also supplement it with Font Awesome.

Why double sidebars? Because Nheko established this pattern and I still think it's a good idea. On the desktop there's usually plenty of horizontal space to comfortably show everything without having to hide things away and require you to click multiple times. Still, both sidebars are collapsible to "just icons" for people who need the extra space.

In fact, most Matrix apps (Element, Discord, ..) have the same sort of "double sidebar" layout, but usually collapse the left-most sidebar to "icons only" by default. I think this makes it hard for new users to learn (icons are cryptic without a label) and there's no good reason to do it when you have enough horizontal space.

As for the padding, whether the defaults look good probably depends on screen size and personal preference. Komai is very configurable. There's a "Density" setting which offers 3 different options ("Spacious", "Compact" and "Dense"). "Spacious" is the default one, because it provides better ergonomics due to larger hit targets. Accessibility is important, but users who find the default padding too much can adjust it.

Disclosure: I've been working on Komai in my spare time for a few months now.