Erased disk but can’t reinstall Mac hd, I only see base system in disk utility

Look for the View button and select Show All Devices.

If you then get a device, select it and Erase. Use GUID partition Map and APFS format.

Base System is the Recovery volume.

Any idea how old it is? I.e., it's not a 2020 or later model, is it?

Erasing the entire drive on Apple Silicon will completely disable it. Those only came out in 2020.

Are you booted into Internet Recovery? Restart and hold down cmd-opt-R. When prompted, connect it to the internet.

You should see a spinning globe as it boots from Apples Servers.

So I need to select OS X Base system and erase it. Use GUID and APSF and name it?

No. That's not what I said. Select the Device, ST31000528AS Media

For the disk format, use Mac OS Extended (Journaled) instead of APFS.

Again, erase the device. I don’t know why you are seeing OS X Base System on the internal drive.

What is the top device name. I can't read as the image resolution is too low.

That sounds like your internal drive. I don't know how you got OS X Base System for a volume name.

Select it and Erase. Use GUID and APFS. Name it whatever you want.

It looks like there is a lot more to it than just Media.