Tower Controller reported directing a go-around due to a landing aircraft still on runway due to incorrect taxiway exit instructions issued by the Controller.

Narrative

Aircraft X landed RWYXXR. I intended to instruct them to exit TWY 1; but instead said TWY 2 and missed it in the readback. Aircraft Y was on short final when Aircraft X indicated that they were not clear of the runway. I instructed Aircraft Y to go around immediately; but they did not respond promptly; so I reissued the instruction. Despite Aircraft Y not responding; it appeared as though they had already started the go-around prior to my second call. Oddly; the ASSC (Airport Surface Surveillance Capability) did not alarm; although Aircraft X did appear to be fully clear of the edge lines.I was heads down trying to manage MIT (Miles In Trail) assigned by ZZZ TRACON; didn't catch the unintended instruction and readback; assumed the Aircraft X had taken TWY 1; and did not catch it in my scan. There were a multitude of errors that I made; largely due to my distraction with the MIT. Aside from my errors; the ineffectiveness and unreliability of the ASSC to alarm when necessary and give us false alarms is highly problematic and concerning.