Please try re-downloading the game. If you can't progress, please try to create a clean, new profile. It is possible an old profile or old game files is causing this behaviour.
Viewing post in Manic Miners: A LEGO Rock Raiders remake comments
Solved: Beware of Network Drives.
The problem persisted after re-downloading and starting a new profile. So I started brainstorming, thinking that my setup could be the problem, and immediately it be became obvious.
My downloads folder is on a network drive, and I extracted the game files there and ran it. So I moved the game folder to my C drive, and now the vehicle menu works great.
Thank you for your support, It was just a silly mistake for me to try running it from a local network.