Funky tire question

Hi all, roadie/mtber coming in peace. I am putting drop bars on my hardtail and would love some recs for very funky tire requirements. This bike will be doing about 10-15% on road/tarmac, 60% on gravel, and 25-30% on singletrack. I am pretty set on putting a fast XC tire up front, and a grippy gravel tire on the back, and wanted some recs on tires. On the front, I'd like something I can feel very confident cornering singletrack but also rolls fast(ish) on hardpack/tarmac. On the back I'm thinking something knobby on the edges but relatively smooth in the center.

I am currently thinking about a 2.2 (55ish mm) Conti RaceKing on the front and a 50mm (2.0ish) Conti Terra hardpack on the back, but would love any recommendations as I don't know much about XC/Gravel tires. The tires are gonna make or break this build so would love any information. Thanks!