I have a Samsung S23 Ultra (for the CPU for emulation + the 5G modem). It doesn't even have a clock/alarm app.

Idk, mine has it. You must have some kind of alarm/clock functionality somewhere. The time picker is normal scrollable hh-mm-ss, right? On a Pixel, it's something like an analog clock but also not.

I also can't look on the Pixel anymore, but I remember there were weirdly two different control centers that always got me.