So I came across this question asking about how the make the Earth hit the sun. It has many similar posts like this one about changing the moon's orbit or this answer about moving asteroids which could be generalised to apply to the problem. There may be a lack of research and other problems, I'm not disputing that, but why is that question broad where a similar question isn't?
But how big should the rocket be?
Which kind of rocket?
How far away do I need to be from the collision?
How much will this cost?
Where should I place the rocket/engine?
Do I need multiple rockets?
It ends in a litany of questions, not a question. It asks what kind of rocket without any indication of the tech level or other rules. It asks about cost without any indication of the economic context.
The question you note is not at all similar,
What artificial disaster could disrupt the orbit of our planet?
But if you wondered what could cause the Earth’s orbit to shift (not limited to kinds of rockets) it might be what you want to know. Then you can follow up (e.g. how much would xyz cost?”) with a specific scenario referenced as xyz, adding details about your economic system.
No the question isn't too broad. Anyone answering the question only has to apply the rocket equation to a "vessel" with the mass of planet Earth. This will provide a ball park figure for the requirements of rocketry to deorbit an astronomical object moving at 30 km/s.
It should be possible to calculate the mass ratios for a range of rocket propulsion technologies: chemical rockets, ion and plasma propulsion systems, fusion plasma rocketry, and, if necessary, photon drives.
Doing so, it will give a concept of how feasible the proposition. At a guess it won't be feasible as the mass ration will be comparable or far in excess of the mass of planet Earth.
The list of the other questions are only subsequent considerations arising from the initial question about using rockets to deorbit the Earth to crash into the Sun. For example, if this is a practical impossibility, then it becomes irrelevant to work out what the economic cost of the operation would be. While it is a given that the mad scientist has unlimited resources, this is only noise in the signal of the primary question and may be sensibly ignored by anyone attempting to answer this question.
The question is not too broad because its key premise can be analyzed by an application of the rocket equation. Everything else flows from that analysis.