I can’t get my phone to backup to my iCloud on my computer.

If the phone states that it was backed up, what do you mean by "it showed no activity on there in"?

Note that you cannot view the contents of an iCloud backup but you can view how much storage space the backup is using. See: Manage your iCloud storage - Apple Support

In addition to backing up to iCloud, you can sync selected things to iCloud (e.g., Contacts). For that to happen you need to turn the desired options on in Settings > [username] > iCloud > [e.g., Contacts] and the sync should happen automatically. You can verify that data has synced -- use any computer internet browser and log in to www.icloud.com and look in the apps there (e.g., Contacts).

See these articles Get an Apple Music Family subscription - Apple Support

If your iTunes backup couldn't be completed or you can't restore from a backup - Apple Support

Restoring from an iTunes or iCloud backup when a later version of iOS is required - Apple Support

I may be misunderstanding but iCloud isn't on your computer. You can backup an iPhone directly to iCloud without any need to use a computer and/or you can backup your iPhone to a computer via iTunes with no involvement of iCloud. See the following:

How to back up your iPhone, iPad, and iPod touch - Apple Support