So when viewing Epsilon frontend on mobile, there is a search icon in the header/navbar. I don't understand why that is not on the desktop navbar. Is there a way to add it? I want search to be easily accessible from any page on the site.

I would say it is essential on desktop... But you are free to go with uodates and tuning of theme based on your needs!

If it is essential on desktop, then why is it not there on desktop?

To be clear, I am pointing out that the search button is not available on the navbar on desktop, but it is on mobile. This seems like a design mistake. Can this be fixed in an official update?

Essential how it works

I don't understand what you are saying.

Simply said, if you want to modify something, you modify it and do not ask to add your customization into theme.

OK, simply put, the developers of this theme made a design error. It makes absolutely no sense to include a search button on mobile, but not on desktop. So I was pointing that out much like I would point out a bug, as it seems like an obvious mistake. If there is no interest in fixing that, then understood, we will take care of it ourselves. But it is somewhat surprising given how polished most of your plugins/themes are. 

It does not look like error or bug.