In the UK the arrests are mostly about "grossly offensive" speech. That's more of a grey area than the clearly defined hate speech. Often there are arrests and investigations but convictions on these are less. Convictions of hate speech also occur but are not news worthy and no one objects. The two different offenses are being confused and so it becomes news. In the US they don't have the grossly offensive category.
It's an issue because people are being investigated because people are offended by some things while others are not, and others (like comments here) see the difference between offensive speech and outright calls for violence. The police in some areas are encouraged to actively investigate reports of offensiveness whether or not they seem to them serious. It's a good idea on paper but the ambiguities and unequal application of their policy is newsworthy. It leads to conspiratorial and political theories.
There is also a related newsworthy issue of the widening of what hate speech means to encompass forms of offensiveness. So some may say it's a direct call to violence to say some things but others may say it's not. This ambiguity leads to an effect and discussions.
"Silence is violence" and "From the river to the sea" are topical example quotes used in this debate.
Yeaaaah, the Communications Act 2003 is not fit for purpose in the modern information age where [seemingly] the vast majority of conversation is taking place in digital spaces. Sidenote, I do think it's amusing how, prior to the Online Safety Act 2023, it was an offence to Cunningham's Law someone (posting a knowingly-false statement online to annoy someone into correcting you). That said, I'm more or less ambivalent about "grossly offensive" speech: most of the examples I find people moaning about are people being gratuitously abhorrent and should have known better. But again, there are examples of police and prosecutors getting it wrong.
But I think the leap from acknowledging that to "speech should never be infringed", as many freeze peachers would advocate, to be infinitely more destructive: just see what it's doing to America. Just look at what the infiltration of American-style freedom of speech principles is doing to this country: we have people defending Lucy Connolly, the woman who publicly advocated for the burning down of hotels housing asylum seekers, calling her a "political prisoner", that the government is "silencing the right".
One part where I agree with you is "From the river to the sea": there are two versions of this (more than two, but they are variations of the same thing), the first being "From the river to the sea, Palestine will be free", and the other "between the Sea and the Jordan there will only be Israeli sovereignty". Guess which one our government finds objectionable. And guess which one is being used to justify a genocide. It does bother me that the government can chill and punish speech that objects to its foreign policy. But I feel as if (this is just vibes, feel free to correct me) the most harm being done is through anti-protest laws, not grossly offensive digital communications: I personally know of multiple people who regularly post abrasive, if not downright virulent "silence is violence" type content online, but do not go to protests because they fear arrest, detention, and being fired.