HOW DO I CONNECT A USB DEVICE TO MY 16 INCH MACBOOK PRO M2 2023?

USB comes in many flavors that have been refined/improved over the years.

The original USB socket (known at USB-A) was successful, despite how awful it was (you were pretty much guaranteed to take three attempts to insert it the right way).

At the same time as USB-A was USB-B, designed for end-devices only (such as a printer), but that was a pretty stupid idea since it didn't offer any advantage over the USB-A socket, except for cable manufacturers that made more money by selling extraneous cables.

After that, people realized that the USB-A socket was oversized for what it could do, so variations such as Mini-USB and Micro-USB came alone, the latter being pretty ubiquitous.

All of the above are keyed and suffer from requiring too many attempts to orient the cable the right way around.

This problem (as well as other limits of the standard) was finally solved by USB-C (taking notes from Apple's Lightning and Thunderbolt ports) which are smaller and can be inserted either way around.

USB-C has very quickly become the standard, and that's what on all MacBook Pros now.

Under the hood, there is a lot of tricks played to maintain compatibility, so your 10-year old USB drive can be plugged into a new USB-C port and still work - you just need an adapter to convert the physical USB-A socket to a USB-C port.

Apple sell this one: USB-C to USB Adapter - Apple

but many other vendors also sell similar devices.

The message you quote implies that you had it set correctly - the drive was attached to your Mac, and that two things are at play here.

First, recent versions of MacOS default to not showing external drives on your desktop. While this can reduce clutter, it also makes it harder to track what disk(s) are attached.

You can toggle this in Finder Preferences -> General where you can select which items to show/hide on the desktop.

The second part is the warning you got about not properly disconnecting the drive. Since you just unplugged the cable (assuming it wasn't working), the OS is warning you that this could damage the drive, or files on it (if a file were in the middle of being copied there, for example, it would be incomplete if you just unplugged the drive). For this reason it's recommended that you unmount the drive first (by dragging the disk icon to the trash/eject icon on the Dock, or by clicking the Eject icon along the disk's name in a Finder sidebar.

At the end of the day, the risk is low, but not nil, so generally better to unmount drives before disconnecting them.

I'm assuming from what you posted is that this USB device has USB-A connections. If so, you just need to get a USB-A to USB-C adapter to connect the device's cable to your new MacBook Pro.