When your AirPods are inside a closed case, they enter a low-power state to preserve battery, which often prevents them from maintaining a live connection to your iPhone. This is likely why you see a location from several minutes ago but cannot "Find Nearby" or play a sound—the AirPods aren't currently "awake" enough to communicate with your device.
Find My usually displays the last location where the AirPods were last connected to an Apple device. If they are in a closed case, they won't typically update their location in real-time unless they are moved and detected by the Find My network (for supported models like AirPods Pro 2 or AirPods 4 with ANC).
Your best option right now is to mark them as lost in the Find My app. Open Find My, select your AirPods, and under "Mark As Lost," select "Activate." This will allow you to leave a phone number or email for whoever finds them, and you'll get a notification the next time their location is updated. Keep checking the map, as the location may update if someone opens the case or moves them near another Apple device.