Since I started to join other communities like Writing, English Language & Usage, etc. I always noticed something that made my UX a little bit confusing, the home page button redirects to Stack Exchange, not the current community.
In Stack Overflow, if I want to go back to the main page, I do click on the Home Page Link. For example:
However, in other communities, it looks like this:
As a Stack Overflow user, I'm more inclined to do click on the StackExchange Logo by default. I always forget that the link in other communities doesn't have the same purpose.
I could suggest just a simple text like Writing for the button.