Not 100% sure but it looks like the following linked download is for all Logitech receivers. A firmware update targeting the receiver may work and also it should be found since that only has to be plugged into the USB port and correctly working from that. I can't really tell if the m220 is offered firmware updates though.
https://support.logi.com/hc/en-za/community/posts/360033207154-Logitech-Unifying-Receiver-Update or direct https://support.logi.com/hc/en-gb/articles/360035037273
You can also ask there on their forum.
I can only think that your Windows installation is messed up and needs to be reinstalled or something like AntiVirus (or something else) is blocking the driver install. With more emphasis on the first :)
Logitech doesn't offer a separate driver as it simply uses Windows provided mouse driver on first connection.
Oh, one side point. Its wireless. Its needs to be in close range to the usb receiver. Like keyboard close to the mouse. Closer than the computer if its a desktop. I've never tried seeing if wireless mice have issues on first connection of the receiver if there's a bad connection but its a theory.
Its possible there's some sort of driver issue. Maybe someone else will try to get that sorted should it be. But, there be a question what happened in the first place. I'd say just clean install and start fresh. But, see what happens and try the smaller things first if that's your desire.