Any mouse and keyboard recommendations with good configuration tools on Linux Mint?

Before replacing the Logitech gear, try Solaar. It's a Linux utility for configuring supported Logitech devices and receivers, and you can find it in Mint's Software Manager.

It doesn't recognize every device, though, so check whether yours show up before counting on it for configuration.

For the keyboard, look at models that support QMK and VIA rather than picking a brand on its own. VIA can configure compatible keyboards in a browser, although browser support matters. Chrome supports the WebHID feature it uses, while Firefox does not.

Check the exact keyboard model for VIA support before buying. That recommendation doesn't really solve the mouse side, though.

Basic mouse and keyboard input is one thing, but a dedicated Linux app for changing hardware settings is another. I'd check support for the exact model and the features you want before buying, rather than assuming a whole brand will work with a particular utility.