Typescript Recursive String Interpolation

I'm working on a simple (but hopefully type-safe) system that represents timeSlots as strings.

// example
const t1 = "|mon::10:30|";
const t2 = "|fri::20:00|";

So far I have managed to type these timeSlotStrings using string concatenation:

export type Weekday = "mon" | "tue" | "wed" | "thu" | "fri" | "sat" | "sun";
export type TimeSlot = "08:00" | "08:30" | "09:00" | "09:30" | "10:00" /*...*/ "19:30" | "20:00";

export type TimeSlotString = `$|${Weekday}::${TimeSlot}|`; // <- there you go!

const t1: TimeSlotString = "|mon::08:00|"; // OK! ✅
const t2: TimeSlotString = "|sat::17:30|"; // OK! ✅

But now I need to type the resulting string of concatenating TimeSlotString many times. The type should be called TimeSlotsConcat but I'm not sure this is possible, if it is, then what the syntax would look like?...

// example:
type TimeSlotsConcat = 🤨❓❓❓ // <- what type would satisfy s1 and s2?

const s1: TimeSlotsConcat = "|mon::10:30||tue::14:30||wed::08:00|";
const s2: TimeSlotsConcat = "|tue::11:00||tue::14:30||thu::18:00||fri::12:30|";

I tried using the TimeSlotString type recursively, but no luck...

type TimeSlotsConcat = "" | `${TimeSlotString}` | `${TimeSlotString}${TimeSlotsConcat}`;

//  ❌ ERROR: Type alias 'TimeSlotConcatStrings' circularly references itself.

So here goes the QUESTION: Is there a way to represent TimeSlotsConcat in typescript?