In the final episode of Game of Thrones, a pivoting moment resides in
A gathering where all greatest remaining Lords & Ladies of Westeros are presented Tyrion and Jon Snow by Grey Worm, in order for them to be judged.
I don't understand how the Council made up by the remaining Lords & Ladies was so merciful with Tyrion and so harsh for Jon Snow.
First, it seems that Grey Worm and the Unsullied (which for some reason have not executed the two prisoners the moment they found out they successfully conspired to kill their queen, and waited for a trial gathering Lords of the kingdom to be assembled) hold a lot of authority on the prospects of the prisoners, and almost hold as hostages the Lords & Ladies.
However, as the scene unfolds, it seems they decide to fall in with the Council's authority on its own lands.
As such, they accept to see Tyrion go from allegedly sentenced to death for treason to choosing the future of Westeros and becoming the Hand of the new king, as it's what the new king and the rest of the Council wants.
However, Jon Snow is most severely punished by a life-long exile in the Night's Watch (taking the black being often represented in the series as an ultimate choice with death). But most of the Lords & Ladies at the table are in fact on Jon's side, or, if not exactly, are at least expected to have been horrified by Daenerys's slaughter and wishful for her cruel reign to end. In fact, we're very much in the same situation as with the Mad King prior to Robert's Rebellion. When Jaime Lannister killed this king, judged by most as a tyrant, he was pardoned by the new king and remained a King's Guard knight.
At the gathering, except for Grey Worm which seems to respect the Council's decisions, only Yara Greyjoy seems to be unhappy about Daenarys's death. Though, her opinion is of light importance as, as opposed to a lot of others present in the Council and particularly Jon's allies, she has played a very little role in the Long Night and the attack against Cersei.
How come Jon was punished for killing a queen almost everybody judged as a tyran deserving to die, and not honoured for having accomplished the only move leading to potential peace in Westeros?
All the more so when the two persons that can truly decide his fate – the King and his Hand – are his brother and the man that convinced him to kill the queen to save the Realm?
Finally, as discussed in comments for this question, Jon is at this moment the true heir to the throne, and an important part of the Council is aware of it. In fact, the plot insists heavily on that Daenerys decided to reign by fear because she was afraid that the people of Westeros would turn to Jon, who they like better and who has a better claim to the throne. But when she is ruled out, this much advertised turn of events strangely doesn't take place.
Edit: I don't believe it's a duplicate of this question, as my question asks why the judgement for Jon is so harsh, while the other one asks why Tyrion judgement ends up freeing him. Those are two different characters, and I can't see the answer to the other question that would apply to this one.