Need detailed help on how the Apple Business Program works
The steps you describe are correct, yes. There's however no need to do it manually like you describe - you can just choose Distribute in Xcode to automatically send your archived build to Apple. Just like you would if the app was going on the App Store.

The difference between putting the app on the App Store, and doing what you want, is simply this one step: On App Store Connect in the "Pricing and Availability" tab for your app, you have to select "Available privately as a custom app for business". This marks your app as private and makes so that the public cannot find it on the App Store.

When you have selected that it is a private, custom app for business, you'll be prompted to provide the IDs of the customers you want to be able to get the app. When you publish your finished app, those customers will see it in Apple Business Manager.

The customer will be able to buy the app, and install it on devices using either MDM (centrally install the apps) or using redemption codes (where the enduser enters the redemption code on the App Store).

There's no special "link" that you need to provide to your customer.