When the Fetch Altitude For Coordinates button in the Location tagset of the Metadata panel is pushed while in the Map module, it correctly sets Altitude but it doesn't display it in the Metadata panel. This appears to be an old bug filed in 2019 that didn't get migrated from the old feedback forum:
https://community.adobe.com/t5/lightroom-classic-discussions/map-module-altitude-of-the-points-si-0-...
To reproduce on LR 13.2 / Mac OS 14.2.1:
1. In Library, select a photo that doesn't have any assigned GPS coordinates.
2. In Map, drag the photo to the map. Observe that it gets assigned GPS coordinates but not Altitude (correct).
3. Click the Fetch Altitude For Coordinates button. Observe that the Altitude field remains blank (incorrect).
4. Go to Library and observe that the Altitude field is filled in (correct).
5. Go back to Map and observe that the Altitude field is filled in (correct).
See the attached screen recording.