One of my books features an immortal protagonist and I've as such thought about this quite a bit. More than the answers already provided here, what I found interesting as a writer was the balance I needed to find between making an immortal detached from mortal values while still being engaging to mortal readers.

Said as a pithy question, if you can outlive everyone's decisions and mistakes, what would it take to make you do anything at all?

I think you're undervaluing loneliness. Loneliness isn't just missing some one. Loneliness means there's no point in connecting with people because they will just die. Loneliness means that no one knows the depth of your condition because it isn't available to them. It means that as they change and face new obstacles, you'll be oblivious to all of that. You'll not only see them die, you'll see the vitality deep out of their pores as they age. All the while you'll never know what that means personally or feel that slow slipping.

Also, super weird that your example is a breakup and people dying is something not worth registering.

I'll say no one can truly know. Unless you are yourself immortal

Loneliness. I think being immortal would show someone what true Loneliness is

I suppose it depends on the rules of this specfic immortality. As someone who lives with chronic pain that literally never feels physically comfortable in any position, immortality sounds like a cruel joke. Not that I'm suicidal or eager to die, but the fact that it would progressively get worse and worse without any sort of end is.... horrorific.

Does yer dick still work when you’re like 150?

Read this on the largest number every used in a mathematical proof.

Then ask yourself, if you think you could handle this number in microseconds let alone an eternity

https://waitbutwhy.com/2014/11/1000000-grahams-number.html

LoL investing and compounding! I literally have all the time in the world.

If it's just you being immortal, loss of all family, and friends, and loss of new friends, rinse repeat forever. Eventualdieyoull watch society collapse and regrow (possibly), and the planet will die. Immortality is forever after all. Then you're left alone on a deserted dead planet. Electronics you have will eventually break and fade away to time. The sun will grow and die off, and it'll burn because you're immortal but still stuck on a planet that'll get enveloped, eventually. Living forever would be terrible unless it was forever until you died of something physical, just not age and illness.