The AirTags are identified as "items" per Apple. As such when using the Find My app on either an iPhone, iPad, or Mac, they would appear on the Items tab of that app. Note that iCloud's Find My does not show items at all ... not sure why Apple did this.
When you leave an AirTag behind (outside of the Bluetooth range ~30-40') of your iPhone, it should retain its "last known location" for up to 24 hrs. After that, they would show up as "No location found." Then the only time you would get updates, is if another iPhone gets within Bluetooth range of your tag.
One means to try finding it, would be if you know the rough location of where you left your keys, you could use your iPhone to locate it with the Find My app. If you have an iPhone 11 or newer iPhone, you can take advantage of its "precision" finding feature which relies on Ultra-Wideband (UWB) technology, in addition, to Bluetooth to locate it.