I have healing prediction turned on for both "Player" and "Target", and it does not show the healing prediction for either.

I had invited people to my group to see if I had to have the person that was healing in my group, but that did not work either. The opacity setting is also maxed out at 1 for both "Player" and "Target", but I still do not see it.

I do not have any sort of Healcomm addon or any unit frame addon that has built-in healing prediction.

It was working for me when I was raiding earlier this week, but it does not seem to work when a random player would heal me, or if someone would heal me when I was in a party.

Is it supposed to function like that, or is there a way to make it so healing prediction would work outside of being in a raid?

The only way for it to work is if both players have an addon that includes healcomm and are both grouped in a party or raid. Unfortunately that is a limitation that can't be changed in classic wow. But, I think you should see healing prediction on targets even if they don't have healcomm though.

This is what is looks like when you heal someone without healcomm. You can only see your own healing predictions.

This is what happens when someone without healcomm heals you or anyone else. You do not see any predictions.

If you know the person you can ask them to install an addon like
https://www.curseforge.com/wow/addons/healbarsclassic-hotfix

Healing prediction should work on all targets. Make sure you don't have healcomm included in a separate addon because that could cause issues.

Ah okay. Got it. Thank you for the clarification.