Governments shouldn't be in the business of deciding what is truth and what is "misinformation", and they certainly shouldn't be punishing people based on the outcomes of such determinations.
Otherwise, we'd have to ban the church and jail all the priests.
As for the punishment, it could be as simple as community service or losing access to public benefits for some time.
“Doctors are killing people with the vaccine?” Ok, find and pay for your own doctor, you’re not welcome in public hospitals.
To engage with your point tho, who is to blame for the spread? the person who posts the disinfo or the programmers who decide the disinfo is good for engagement?
What about people saying you should be wearing masks at the beginning of the pandemic, when the CDC and WHO were saying you didn’t need them?
Anything can be "classified" as anything if you draw your venn diagram circles big enough; that doesn't make it so. Furthermore, "terrorism" isn't itself a crime, the violence that usually comprises it is (such as murder, bombings, et c). A rather good thing that, or otherwise people like yourself would love to "classify" more things as something illegal, bypassing the actual authority in our society tasked with making new laws.
Spreading falsehoods is protected expression, at least in the US.
There are people who are deliberately spreading misinformation to make money. I think that we absolutely should be investigating and prosecuting such people. We simply lack the policing resources to effectively combat online fraud, online bullying, and online extortion. I think we need a fundamental restructuring of policing on our society to make this feasible.
The US constitution prevents bans on televangelists.
In the US, to achieve your goal you'll have to start off with a constitutional amendment repealing the first amendment.
There is a long history of the US courts abrogating free speech. "Shouting fire in a crowded theater" originated as a metaphor to justify preventing pacifists from distributing anti-draft pamphlets.
If the televangelist can be demonstrated in court to not believe the stuff he is telling people to make money, I see no reason why fraud charges shouldn't stick.