Assuming we're talking about the typical example (https://youtu.be/WkZGL7RQBVw) - in the HUD, altitude is the right-hand vertical tape. (The left one is airspeed.) It looks to bottom out around 4400 feet during the AGCAS recovery.
I'd need to look it up to be sure, but I would assume by default that this is a radar, not a barometric, altimeter.
(To expand on that: A barometric altimeter works via air pressure, and thus shows height above sea level; a radar altimeter measures the time taken for microwaves to go from it to the ground and back, and thus shows height above ground. I wouldn't be surprised to find both types in a fighter, but I would be very surprised to find that a radar altimeter wasn't the default, because it's going to be the one that provides the most accurate information and thus the most useful to a pilot who needs to worry about avoiding CFIT during complex maneuvers.)
The radar altitude is shown further down the right side (the box with the "R" next to it). It bottoms at 2970 as I saw it at with the tape showing 4370MSL.
The right side of the tape is MSL.
If you watch that box through the video, you can see why you don't use the radar altimeter for everything. Any time you don't have clear line of sight to the ground with the belly of the aircraft, the radar altimeter blanks out completely. If you're in a roll, it will give incorrect information as it's not pointed directly at the ground.
