Leafpool "dropping her rank"

even if she did it herself, it was a self-imposed punishment, so I would say that it is a punishment of sorts

although if she made the choice, then the punishment would be lessened by her feeling that she has served justice rather than been pushed from her position, if that makes sense

What even is punishment tho? Feeling terrible or having a leader exile you?

I guess Darkstripe was legitimately punished then and Leafpool wasn't. After all, even though he left with a smile on his face, felt not a spec of guilt, and eager to commit even more terrible acts, a leader exiled him, so he was properly punished. But Leafpool? StarClan no. Her self esteem could be -100000 and she could treat herself like a pile of dirt, but until her dad kicks her out she's got the good life. Shame on her.

What else are they gonna do to her?

Banishment or death.

Imo not really. Not saying she should be killed just like that, I'm more or less speaking of the deathberries scene, or her dying post war with the DF. But banishment? Yeah.

I cannot make myself see Firestar just banishing her. Not just because she is his daughter but also because he doesn't really roll in that way if you know what I mean. Besides if he really did do it, maybe the Clan would be okay with it but Sandstorm and Squirrelflight definetely wouldn't. They would either leave with Leafpool or Sandstorm would simply break up with Firestar (very possible) and Squirrelflight would just stop talking to him.

They only got banished because their leaders were mean, and in Brokenstar's cause evil. If Firestar was mean like them she probably would have been kicked out too.

I think her punishment was enough (heck, she was planning to kill herself over it). Plus, what is banishment and exile used for? Cats who are actively a threat to the clans (Mapleshade was debatable, but more on that later). Leafpool may have broken two codes, and temporarily abandoned her family, but she was never putting the Clan in danger. Not to mention that her kits were the ones that saved the clans (well, two of them anyway) so it did more good than harm.

Also on the subject of Leafpool being exiled, who was the last cat that we know of who was exiled for having half-Clan kits? Mapleshade. And what happened when she was exiled? She lost her kits in a moment of panic and desperation, lost her mate, and held resentment towards her Clan. That led to her becoming the infamous murderer the books show her to be, one of the most dangerous characters in the entire series. And knowing how low Leafpool’s opinion of herself was at the time the secret is revealed, who's to say she wouldn't do something like that on impulse?

And what would happen to her kits if she was exiled? They were fully grown, so they would suffer too. Jayfeather was shown having resenting Leafpool when he found out about her lie, so can you imagine how much more that resentment would be if she was exiled? Hollyleaf was well on her way to becoming evil, so exile would have just made that even worse (probably, she would've gotten exiled herself, or killed even more). I don't remember too much about Lionblaze, but considering how bloodthirsty he can get with his powers and that he already trained in the Dark Forest, I feel like it would be very easy for the Dark Forest to take him again.

So basically, I feel like something like banishment or death would have been too much, and would've had horrible consequences for the rest of the clan because the kits are grown. The only thing that should have happened was that Leafpool should not have been given her medicine cat position back, because that undoes the idea of the punishment. I think the only reason that was done was because Leafpool was repeatedly shown to be a poor warrior, and was of little use to the Clan that way.

As for whether she should die, I honestly don't see any reason for her to die. Thunderclan may have three medicine cats, but it's implied one of them will move to Skyclan. Not to mention, I don't think Leafpool is that old…