A Boring Dystopia

The Nazis also came to power democratically.

That's not how it works. You can't scream Nazis any time any government does anything. That's not what fascism is nor is it what tyranny is. You're just devaluing the meaning of these terms and showcasing your ignorance.

Just because something is a law doesn’t mean anything.

On the contrary, it matters a lot. The very foundation of liberal democracies is based on the idea that laws are everything. Nobody is above the law, everybody is equal in the eyes of the law, and the law is the public's will. You can agree or disagree with individual laws, however, that doesn't change the facts that laws are the source of legitimacy.

The UK here isn't ignoring it's laws, it's not creating new laws to target specific groups, nor is it using these laws to wrongly punish people who did nothing wrong. Their terrorism laws have been created by democratically elected politicians who reflect the will of their people, the laws they created and voted upon are universal and well defined, and these laws have been established law for decades.

This groups intentionally violated these laws, they knew what they were doing, and now they're facing the consequences of their actions. This isn't tyranny, this is a normal society punishing criminals for breaking the law. This also law isn't immoral because it seeks to ban harmful behavior in a fair and universal manner, and the punishments for these violations are all reasonable.

It’s also quite telling if your national security is tied to genociding children.

You don't seem to get it. Being self righteous doesn't give a free pass to be a terrorist no matter how you noble you think your cause is. If you excuse terrorism based on your ideological biases, then you don't even have any ground to stand on because your position isn't a principled one. No country is dumb enough to excuse group seeking to undermine their authority, damage public property, threaten national security, violate their laws, and sabotage public property, and rightfully so because they'll be inviting chaos, violence, and instability into their societies.

If they gave this group a pass then they'll be setting a precedent that other self righteous groups can get away with terrorism if they act like their cause is noble enough to be above the law. What kind of disastrous future would that bring? Are Russian Sympathizers now excused to go bomb the parliament when it's out session because they don't like the UK supporting Ukraine? Are Chinese sympathizers now excused to damage the London Bridge because the UK supports Taiwan and Tibet? Are a far right groups excused to sabotage the PJHQ because the UK supports immigration? Of course not, because that would be really, really stupid. If you do something wrong, you're going face the consequences for it, simple as.