My iPhone made a backup last night but nothing shows up in the list or on iCloud. Where is the backup?

You can verify existing backups in Settings->Account(top of settings)->iCloud->Manage Storage->Backups->Device Name on an iOS device.

To use one to restore from, you must have already reset the device to factory settings and are in the process of setting it up again. At that time you you will get a choice to restore from a backup in the Apps & Data screen.. When selecting to restore from an iCloud backup it will show a list of backups available for you to choose from.

Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

lisaschultz6684 wrote:

My iPhone 8 made a backup last night but nothing shows up in the list or on iCloud. Where is the backup?

It just says "Last successful backup: Yesterday at 5:36 PM"

That is your confirmation that your device backed up.

Backups have never been able to be restored without being in the device's setup process. It has never been a thing you do on the device once it's been set up.

It's always been a thing you do during setup of the device. Apple has changed nothing.

lisaschultz6684 wrote:

So that was a bust. I was able to restore the old backup from Saturday, but the data from before that date is still not back on the phone.

I have Messages backup active.

I had the Messages from a contact all visible before the Saturday backup.

Then the iPhone does the backup on Saturday and all the text messages from before are gone.

Even now in the restored backup, they are gone.

"Nice" software.

icloud backups up whatever data is on the phone, not what isn't on the phone.