In this heavily related question: Why did Agent Johnson try to kill the Key Maker?
The asker asks (bold emphasis mine):
Agent Johnson (the one who fights Morpheus on top of the trailer) tries to kill the Key Maker which doesn't make sense since the Agents are programs inside the Matrix and The Key Maker is essential for The One to get to the source. Components of a system work together to achieve a mutual goal.
The answer there explains how the agents likely aren't "in the know", which may explain why they might not be a reliable source of information regarding whether or not the Key Maker is actually an exile. But either way, they clearly believe he is an exile, and apparently an important one at that:
Agent Johnson: The exile is the primary target.
Agent Thompson: Find the exile.
"The exile" can only refer to the Key Maker, which is made clearer by the fact that Agent Johnson tries to "delete" him once he thinks he's dealt with the humans:
Agent: You are no longer necessary.
Keymaker: We do only what we’re meant to do.
Agent: Then you are meant for one more thing. Deletion.
On the other hand, the Oracle tells us he's being held prisoner, and whilst it's not impossible for one exile to hold another exile prisoner, to me this might imply that the Key Maker is not actually an exile:
The Oracle: Then Zion will fall. Our time is up. Listen to me, Neo. You can save Zion if you reach The Source, but to do that you will need the Keymaker.
Neo: The Keymaker?
The Oracle: Yes, he disappeared some time ago. We did not know what happened to him until now. He’s being held prisoner by a very dangerous program, one of the oldest of us. He is called the Merovingian, and he will not let him go willingly.
Also note that, whilst obviously not official, the Matrix fandom wiki page on the Key Maker lists him as an exile, and various Q&As on this site speak of the Key Maker as though his status of exile is correct.
Whereas the other Q&A is more focused on the motives of Agent Johnson (or any of the agents trying to stop the Key Maker, for that matter), my question is about whether or not the Key Maker really is an exile.
If so, how does that make sense given that he's an essential part of the Path of the One? How else was Neo supposed to meet the Architect if the Key Maker is apparently now an exile and not part of the system anymore?
If he's actually not an exile, what evidence (besides that he seems to be the only way for Neo to meet the Architect) suggests that this is so? I guess the agents were simply not told the truth to create the illusion of opposition, as the answer to the other question states...