A question to the rabbi, and a request for forgiveness.

Rabbi Mazuz does indeed bring some interesting evidence, including the meter and rhyme of ancient piyyutim, which cannot be reconciled with Ashkenazi pronunciation.

What does it mean to “act as you thought”?

When I talk about someone, and say things about them in a harsh way, for example the well-known saying by those who don't listen to what you say and only make headlines, that you are an apostate, isn't that considered an offense? (I know you're interested in the Karpas)

Literally. If he thinks I am a heretic and if he thinks he should take a stand against heretics, then if that is what he did, what exactly should he regret or ask for forgiveness for? He did it to the best of his understanding. If he had not acted in this way, he would have had to ask for forgiveness (maybe not from me).
By the way, for me it is more related to the Haroset.

Isn't this the meaning of slander?

I got the wrong impression about someone, about you in the above example.
I didn't investigate further, because otherwise I would have discovered that you don't meet the definition I know as an apostate, like the above questioner.
Then I started insulting you, calling you names, and giving you a bad name.

The fact that he ultimately came to the opinion that you are not an apostate means that if he had researched from the beginning, he would have come to this conclusion (probably).

(And apologies to Yehuda that it seems like I'm criticizing him, but this is for the sake of understanding)

You're just insisting. If I'm an apostate, there's no prohibition against slandering me. If there's no permission to speak ill of me, then he didn't act on his assumptions and indeed needs to make a confession. Your assumption that if he now thinks I'm not an apostate, that's what would have occurred to him then too, is a very strange assumption, according to which a person never changes their worldview.

It's all well and good that someone believes you are an apocryphal heretic, but on what basis does he believe so?

The insistence is not just for nothing, it is a principle of not accepting slander and checking the details.
Is it permissible for me to accept his words without checking the matter because some writer writes an article about someone who is an apocryphal heretic?

The question is deeper: How much do I have to check what is said about someone before I form an opinion about him? And if you say that it is clear that not every piece of information can be checked, since there is no end to anything, why do you allow yourself to form an opinion without checking? Especially when it comes to something that may be slander? On the contrary, look at every piece of information with an asterisk and don't come out strongly.
Maybe it's difficult, but difficult is not something that should prevent us from behaving correctly.

So you are as rigid as Hallel in the temple?

We repeat ourselves. None of this is relevant. If he checked and came to conclusions and acted accordingly, everything is fine. If he didn't check properly, then of course it's problematic. That's all.