Is there a way using CSS to truncate the text before and after the time from the OWM sunrise or sunset attribute so only the time is displayed on a dashboard tile?
CSS can only truncate text if it overflows a boundary you specify. It can't perform character operations on a string. You'd need to do that in javascript. I really haven't played with Dashboards much so I don't know if you can add javascript or not.
HubiGraph Weather Tile 2.0 does that with the “no title attribute”. It accomplishes it by defining an iframe as an attribute with embedded JavaScript to remove the title.
I know this is not the solution you are looking for but Weather Tile 2.0 can create the display with sunrise/sunset that you want.