You don't have a choice, have to use the one it ships with -- which sadly is still not, in the year of our lord 2023, available with a USB-C connector. Every 6 months or so I do a search thinking "ok, they must have finally made a USB-C Unifying Receiver" but somehow no, they still haven't managed it.
Here's a possible explanation:
...there's sufficient space in the
barrel of a USB-A plug to fit most of the workings of the receiver. The "handle" just contains the antenna, so you get that a, low-profile dongle which you could leave permanently plugged in to your laptop. A USB-C receiver doesn't have all that free space in the barrel and would need a larger handle to hold the gubbins - potentially losing the advantage of being small enough to leave plugged in. Indeed, if you google for wireless mice that do offer USB-C dongles you'll notice that the USB-C dongles
do stick out a lot further than the USB-A ones - and they're probably simpler devices that the Logitech one.
So although there's no earthly reason why Logitech couldn't make a USB-C unifying receiver, if it is going to stick out too far to leave permanently in place then there's not much advantage over just using a compact USB-C-to-A adapter. Plus, many of the Logitech mice support bluetooth anyway - beware 'Mac' editions that don't include the dongle (what is more annoying is that Logitech now have a second, incompatible 'Bolt' dongle system, which is basically dedicated bluetooth...)