Forget about the groove. Bring the white down to meet the black a couple of mm below the groove.
The white paint has a heavier texture than the black area. Tape will never adhere correctly to the white but should be ok with the black render. You may get a little bleed under that needs touching in.
Personally I am not a fan of using tape to create lines. I prefer to use a spirit level and pencil to create a line to paint to in those kind of cases but that works best on smooth walls.