Welp, there the obvious answer based on the premise of working within the system ...
What is Not Forbidden is Allowed
Technically, there is nothing preventing the awakened Dark Lord from entering politics. They have, as of now, committed no crimes nor have they engaged in illegal acts as defined by the laws of the new constitutional monarchy. So long as they are aware of the laws and follow them, there is no reason why an awakened Dark Lord can't enter politics. Believe the people who went over the laws intensely to try to disqualify the Dark Lord -- they found nothing and they dig through everything.
Oh yes, it will possibly anger people immensely -- after all that's a Dark Lord! But the rules need to apply to everyone equally, much to everyone's annoyance.
Odds are that the new constitutional monarchy never considered the Dark Lord regaining their freedom so have never put the appropriate laws into place to safeguard the system from them. Term limits likely wouldn't be considered as that might weaken their own power in politics if they have to retire after so many years.
Difference in Opinion
Given the difference in both the time they ruled and the style of government, the Dark Lord will have different ideas of how to run a nation than the rest of the politicians. On the surface this is a net neutral as they are only one person initially. Even at the head of a major party in the future, it should still be neutral as there should be factions that have differing viewpoints.
Some of their initial views might not be as popular, but theirs was a different time. Harsher justice was needed, and people needed to rule with more power then they do now. But the seeds of those ideas, the ideals of how the Dark Lord may have ruled, are still potentially valid even two centuries later. This is not to say that they should be adopted wholesale, but an avocation of a stronger government on certain things is not necessarily wrong.
Even though their ideas are 200 years out of date, but so long as the Dark Lord can adapt to the changing times in thoughts and deeds, then they can mold the new nation into something that they want to take over and reclaim.
Perspective of Time
The returned Dark Lord want control of their kingdom back, sure. But they can wait -- they are immortal until killed after all. They do not need to reclaim their kingdom tomorrow. They don't even need to do it in a year. They have the option of planning things out over the span of decades and adjusting those plans when the global situation changes. A slow and patient game will suit them best and plays to their strength of longevity -- they can simply outlive their opponents. It's about molding the nation into a kingdom worthy of ruling.
Everything above operates on the premise of entering politics to work up the system to eventually rule. To work within the confines of the constitutional monarchy to amass power and retain it. And done correctly, it could work.
Politics could be a way to gain prestige to begin to hobnob with royalty. Some words here, some money there, and a strategic assassination, and they could be at the top of the monarchy. And as they don't die under normal circumstances, their reign will last centuries. Then the issue becomes how much power has the monarchy given away to the constitution and how could they reclaim it. Same issues, but from the other side of the political system.
This doesn't even get into the murkiness of the fact that as a previous monarch, they are Not Dead. Technically, their rule has been usurped by those that overthrew and sealed them and they could attempt to make a case of it. They might even win depending on how the laws were written.