I would expect it to go into the 'downloads' folder of your browser. That's what happens in Firefox for iOS. It might then offer to open it in an app you have, or offer to find an app in the App Store which is capable of opening a .mid file.

You can also use Apple's 'Files' app to list the files in the browser's download folder. Tapping the .mid file should do something similar.

Like all things in iOS it varies between dead easy and bafflingly complicated.