What you seek may not be viable.
Some (or many) microcontrollers these days come with unerasable factory bootloader. A subset of them can communicate over USB and be programmed with a flashing program on a PC.
The problem is not only about a "driver". Sure the PC needs a driver for the USB device, but the issue is, you need not only a driver like provided by the MCU vendor for the MCU to show up as USB device like DFU programmable USB device, but a custom driver or program to automatically start up and program the MCU with some firmware.
That is a problem, because, as all microcontrollers of same type have identical USB VID/PID pair, the driver cannot know which device was plugged in, so which firmware to program. It might have been a device you manufactured, or some other device, so you can't program a firmware intened to your device to another device which will stop working and there may be no firmware available for that device tha it can be fixed.
Another thing you mention is that like RGB keyboards and mice, Windows not only automatically fetch a correct USB driver for it, it will automatically and forcibly install a program used to configure and control the device. That is a deal between Microsoft and the device vendor to install such a control center, and a security risk. Many such control centers have had gaping security holes that allow bypassing user account control and allowed standard users to become administrators. I was literally shocked by automatic forced installation of such programs even if I simply wanted to borrow a mouse or keyboard and plug it in once for 5 minuted. Computer users are not that stupid that they cannot go to vendor site and download such programs themselves if they need it.
So while a MCU vendor could make a deal with Microsoft to install a MCU flashing program automatically when you plug in an unprogrammed MCU, it is not going to work. The user would not know why this program popped up and what to do with it, or where to get the firmware you need to download to your device.
So while of course possible, you really don't need or want such a driver. Tell users to install the flashing program for your MCU available from MCU vendor site. Then have users plug in the device and make it go to USB firmware update mode. Then instruct users to use the MCU vendor program to upload the correct firmware.
You can also make a program that does all these things for the user without downloading the MCU vendor program, but you need this progra to communicate with the MCU vendor USB driver. So you won't be making the USB driver, just a custom DFU upload program.