Make tab bar icons as in the design (including notification badges)

[DmitryBespalov]

The current 'badge' icon used in the tab bar when there's a new chat message is not as appealing and good quality as in the design.

Can we make it look like in the Figma?

The documentation only allows customizing the text and color.

However, there supposedly is a hacky way to accomplish that which should work. There's also a way to get to a badge view

The downside is that we must add an automatic test to recognize that this hacky way is broken whenever some underlying UIKit changes made and this badge does not work.

[TanyaEfremova]

The tab bar icons are updated in the UI library, as the shared Icon library was tweaked.