Is there an easy way to customize the provided default toolbar?
yes, see here: https://github.com/basecamp/trix/issues/28
Is there a way to make the default toolbar...

...look like this?

And how?
The optional trix.css file provides the default toolbar styles. You're free to modify those or skip them entirely and use your own.
@vahanavagyan, this probably isn't the best place to ask how to copy Basecamp's toolbar.
Most helpful comment
The optional
trix.cssfile provides the default toolbar styles. You're free to modify those or skip them entirely and use your own.@vahanavagyan, this probably isn't the best place to ask how to copy Basecamp's toolbar.