https://youtu.be/omZvd2Vd3PA We built a Kitchen/Wet Bar in a similar, though smaller, corner than you show. The plumbing runs behind the cabinets then below the stairs and connects with a soaking tub positioned on the opposite side. Then waste continues into the sump. This eliminated need to cut concrete. Hope this helps.

Our basement kitchen is significantly different than yours We have a typical bar sink approximately 12x10 for dumping ice and rinsing glassware Nearby we have a large sink used for a variety of tasks from cleaning paint brushes, bathing a puppy or washing dishes (using a separate dish pan). IF you wish a visual they’re included in this video. https://youtu.be/3FqMEqaf0-I

Our bar was actually designed and built, then cabinets fit below. Used IKEA cabinets and trimmed off the drawer to create the low bar. Only oversight was slightly less top bar setback for mixing than desired. Storage was great. Allow sufficient work space, everyone wants yo play bartender. Basement design: Video of basement showing bar: https://youtube.com/watch?v=3FqMEqaf0-I&feature=shareb

I love it! The counters you chose look terrific with the brick. My DH would be in his glory down there :0p