HDMI is a video output only interface. It's used to send a video signal from the Mac to the display. It has no relation to mice.
Why does your mouse have to do with your display?
You connect the mouse to the Mac mini directly. If it's a USB-A mouse, you can use a dock / hub or a simple USB-A to USB-C adapter.
Foe example:
click here ➜ Anker USB C Adapter (2 Pack), USB C to USB Adapter High-Speed Data Transfer for Mac - Amazon.com
or here ➜ UGREEN Dock & Stand for Mac mini M4/ M4 Pro with NVMe SSD Enclosure, 3 USB A 10Gbps, USB C Data Port, SD Card Reader, Silver - Amazon.com
USB is not on its way out, it's just evolved from the traditional USB-A that most peripherals use, into USB-C which is now being built in to Macs like the Mac mini. It's still USB, its just a different type of USB port.