Hey this is really cool! I love how sleek the interface is. We're doing something similar at WhoDB (https://github.com/clidey/whodb) and love seeing all the work happening in this space.
I agree - generalist UIs definitely won't be able to make full use of all specialized features. WhoDB is majorly created for fast developer experience when working with multiple DBs (or even for a single one). I think each database company usually has a specialized tool that they have made themselves (pgAdmin is a good example of that).
Great suggestion on the breadcrumbs, sidebar dropdown, and table count. We have fixed all three of them in our release (in a few minutes).
For table icon and name, we have majorly left name not interactive as users can copy it if necessary - we might add a "Copy to clipboard" type of functionality there. Meanwhile, the table icon will be used to enter the graph from that node and traverse the relationships. Hoping to better the UX together with the community!