First off, the Apple AirTags are identified as "Items" by Apple. Just about everything else Apple sells are "Devices." Yes, a bit confusing at best.
As such, if you use iCloud's Find My, your AirTags will NOT appear under Devices, but your Apple ID-associated other Apple gear (iPhones, iPads, Macs. AirPods) do appear there.
Ok, just to make sure nothing was missed when you initially set up your tags, please take a look at the following support article: Set up your AirTag using your iPhone, iPad, or iPod touch - Apple Support
The other "oddity" is that when setting up more than one tag, we have found that you need to move the first tag that you set up outside of the Bluetooth range (~30-40') from your iPhone/iPad, before attempting to set up the next one. Strange, but we see a number of posts here where folks are having issues setting up their "new AirTag 4 pack."