I don't really know honestly. I don't have set words for those sorts of things.
I tend to give my honest opinion when people I care about are down based on what they are saying, while also trying not to dismiss their feelings about it. I tend to deal with it all factually. If it's related to a bad situation that can be temporary, I'll sometimes mention that it's a temporary, because everything is, and I have found that somewhat comforting in times when life has been hard, but that's about the only consistent thing I guess.

As for self-compassion, it is important or at least stopping self-hatred is, and I'm learning how to do that now, but I'm definitely not there yet. I don't expect it to be easy to stop self-hatred and idk if stopping it is even possible but I still want to hate myself less at least.

I'm also not great at observing my emotions but I don't think it was that I learned to ignore them. I think I'm just not very good at recognising them. I'm more likely to just feel shitty and not know why unless I take time to process what is going on (and even then I don't always work it out) or to think I feel fine but not realise I'm actually not fine until it becomes more obvious.