This is an approach to life sentences I've considered before; I would suggest the prisoner could only petition for execution after being incarcerated for a significant period (20 years or so maybe?) and having exhausted all possible legal appeals. The delay is there to ensure it's not a decision taken in desperation and haste. By that point, if any new evidence to exonerate them is going to turn up, it probably has, although I acknowledge that's not always the case.
I'm not sure I'd equate it to voluntary euthenasia as the prisoner isn't leaving jail alive either way. On the other hand, I can see why linking the two makes sense too.
A goal at which it has singularly failed. There'll be a bit of noise in the papers for a day or two, Stonehenge will be cleaned off with "No harm done" and life will move on with no useful change.
Their stunts were effective the first time or two, but now are largely ignored or even just cause irritation.
If they, indeed we, want to change the trajectory of human caused climate damage we need to build bridges at the community level and bring people together to force the hand of the political class. These stunts don't do that, they just give ammunition to those who seek to prevent positive change.